Quiz

Exponents and Surds

Exponents

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Quiz

Exponents Score: 0/10

1. Simplify and choose the correct answer: ( $\frac{a - 5}{b - 2}$ )³

1. Simplify and choose the correct answer:

( $\frac{a - 5}{b - 2}$ )³

\frac{a 15}{b 6}

\frac{b 6}{a 15}

C. 1

D. None of the above

2. Simplify and choose the correct answer: x^{- 1} + y^{- 1}

2. Simplify and choose the correct answer:

x^{- 1} + y^{- 1}

\frac{1}{xy}

\frac{1}{x + y}

\frac{y + x}{xy}

D. None of the above.

3. Simplify and choose the correct answer: $\frac{5 ( 2a 4) 3}{(- 5a 3) 2 - 5a 6}$

3. Simplify and choose the correct answer:

$\frac{5 ( 2a 4) 3}{(- 5a 3) 2 - 5a 6}$

\frac{1}{2a 6}

B. - a⁶

C. 2a⁶

D. None of the above.

4. Simplify and choose the correct answer: -3 ( ( - 2a³ ) ² + $\sqrt[]{9a 12}$ )

4. Simplify and choose the correct answer:

-3 ( ( - 2a³ ) ² + $\sqrt[]{9a 12}$ )

A. - 21a⁶

B. 21a⁶

C. - 3a⁶

D. None of the above.

5. Simplify and choose the correct answer: $\frac{( x 4) n - 1 ( x 2 y ) - 3n}{( xy ) - 2n y - n}$

5. Simplify and choose the correct answer:

$\frac{( x 4) n - 1 ( x 2 y ) - 3n}{( xy ) - 2n y - n}$

\frac{1}{x 4}

B. 0

C. 1

D. None of the above

6. Simplify and choose the correct answer: $\frac{5 2n 9 3n - 3}{15 2n 3 4n - 1}$

6. Simplify and choose the correct answer:

$\frac{5 2n 9 3n - 3}{15 2n 3 4n - 1}$

A. - 243

B. 1

\frac{1}{243}

D. None of the above

7. Simplify and choose the correct answer: $\frac{9 n + 3 2n - 1}{9 n}$

7. Simplify and choose the correct answer:

$\frac{9 n + 3 2n - 1}{9 n}$

\frac{3}{4}

\frac{4}{3}

\frac{1}{3}

D. None of the above

8. Simplify and choose the correct answer: $\frac{27 3 - 2n 9 n - 1}{81 2 - n}$

8. Simplify and choose the correct answer:

$\frac{27 3 - 2n 9 n - 1}{81 2 - n}$

\frac{1}{3}

B. 1

C. 3

D. None of the above

9. Simplify and choose the correct answer: $\frac{5 n + 1 - 5 n + 2}{5 n + 1}$

9. Simplify and choose the correct answer:

$\frac{5 n + 1 - 5 n + 2}{5 n + 1}$

A. 4

B. - 4

C.0

D. None of the above

10. Simplify and choose the correct answer: $\frac{22009 - 2 2011}{22010}$

10. Simplify and choose the correct answer:

$\frac{22009 - 2 2011}{22010}$

\frac{3}{2}

B. 1

C. -

\frac{3}{2}

D. None of the above

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Quiz Results

Your score is 0 out of 10

Solutions

Exponents Question 1 of 10

1. Simplify and choose the correct answer: ( $\frac{a - 5}{b - 2}$ )³

1. Simplify and choose the correct answer:

( $\frac{a - 5}{b - 2}$ )³

\frac{a 15}{b 6}

\frac{b 6}{a 15}

C. 1

D. None of the above

Correct Answer
Option B

Detailed Solution

Solution Details

Given ( $\frac{a - 5}{b - 2}$ )³

• ( $\frac{a - 5}{b - 2}$ )³

= $\frac{a - 5 x 3}{b - 2 x 3}$

= $\frac{a - 15}{b - 6}$

= $\frac{b 6}{a 15}$

For more info please see

Exponents

Exponents Question 2 of 10

2. Simplify and choose the correct answer: x^{- 1} + y^{- 1}

2. Simplify and choose the correct answer:

x^{- 1} + y^{- 1}

\frac{1}{xy}

\frac{1}{x + y}

\frac{y + x}{xy}

D. None of the above.

Correct Answer
Option C

Detailed Solution

Solution Details

Given x^{- 1} + y^{- 1}

• x^{- 1} + y^{- 1}

= $\frac{1}{x}$ + $\frac{1}{y}$

= $\frac{y + x}{xy}$

For more info please see

Exponents

Exponents Question 3 of 10

3. Simplify and choose the correct answer: $\frac{5 ( 2a 4) 3}{(- 5a 3) 2 - 5a 6}$

3. Simplify and choose the correct answer:

$\frac{5 ( 2a 4) 3}{(- 5a 3) 2 - 5a 6}$

\frac{1}{2a 6}

B. - a⁶

C. 2a⁶

D. None of the above.

Correct Answer
Option C

Detailed Solution

Solution Details

Given $\frac{5 ( 2a 4) 3}{(- 5a 3) 2 - 5a 6}$

• $\frac{5 ( 2a 4) 3}{(- 5a 3) 2 - 5a 6}$

= $\frac{5 ( 2 3) ( a 4 x 3)}{(- 5 2) ( a 3 x 2) - 5a 6}$

= $\frac{5 ( 8a 12)}{25a 6 - 5a 6}$

= $\frac{40a 12}{20a 6}$

= 2a⁶

For more info please see

Exponents

Exponents Question 4 of 10

4. Simplify and choose the correct answer: -3 ( ( - 2a³ ) ² + $\sqrt[]{9a 12}$ )

4. Simplify and choose the correct answer:

-3 ( ( - 2a³ ) ² + $\sqrt[]{9a 12}$ )

A. - 21a⁶

B. 21a⁶

C. - 3a⁶

D. None of the above.

Correct Answer
Option A

Detailed Solution

Solution Details

Given -3 ( ( - 2a³ ) ² + $\sqrt[]{9a 12}$ )

• - 3 ( ( - 2a³ ) ² + $\sqrt[]{9a 12}$ )

= - 3 ( 4a⁶ + 3a⁶ )

= - 3 ( 7a⁶ )

= - 21a⁶

For more info please see

Exponents

Exponents Question 5 of 10

5. Simplify and choose the correct answer: $\frac{( x 4) n - 1 ( x 2 y ) - 3n}{( xy ) - 2n y - n}$

5. Simplify and choose the correct answer:

$\frac{( x 4) n - 1 ( x 2 y ) - 3n}{( xy ) - 2n y - n}$

\frac{1}{x 4}

B. 0

C. 1

D. None of the above

Correct Answer
Option A

Detailed Solution

Solution Details

Given $\frac{( x 4) n - 1 ( x 2 y ) - 3n}{( xy ) - 2n y - n}$

• $\frac{( x 4) n - 1 ( x 2 y ) - 3n}{( xy ) - 2n y - n}$

= $\frac{( x 4n - 4) ( x - 6n) ( y - 3n)}{( x - 2n) ( y - 2n) y - n}$

= x^{4n - 4 - 6n + 2n} y^{- 3n + 2n + n}

= x ^{- 4} y⁰

= x ^{- 4}

= $\frac{1}{x 4}$

For more info please see

Exponents

Exponents Question 6 of 10

6. Simplify and choose the correct answer: $\frac{5 2n 9 3n - 3}{15 2n 3 4n - 1}$

6. Simplify and choose the correct answer:

$\frac{5 2n 9 3n - 3}{15 2n 3 4n - 1}$

A. - 243

B. 1

\frac{1}{243}

D. None of the above

Correct Answer
Option C

Detailed Solution

Solution Details

Given $\frac{5 2n 9 3n - 3}{15 2n 3 4n - 1}$

• $\frac{5 2n 9 3n - 3}{15 2n 3 4n - 1}$

= $\frac{5 2n ( 3 2) 3n - 3}{( 5 x 3 ) 2n 3 4n - 1}$

= $\frac{5 2n 3 6n - 6}{5 2n 3 2n 3 4n - 1}$

= 5^{2n - 2n} 3 ^{6n - 6 - 2n - 4n + 1}

= 5⁰ 3 ^{- 5}

= $\frac{1}{35}$

= $\frac{1}{243}$

For more info please see

Exponents

Exponents Question 7 of 10

7. Simplify and choose the correct answer: $\frac{9 n + 3 2n - 1}{9 n}$

7. Simplify and choose the correct answer:

$\frac{9 n + 3 2n - 1}{9 n}$

\frac{3}{4}

\frac{4}{3}

\frac{1}{3}

D. None of the above

Correct Answer
Option B

Detailed Solution

Solution Details

Given $\frac{9 n + 3 2n - 1}{9 n}$

• $\frac{9 n + 3 2n - 1}{9 n}$

= $\frac{( 3 2) n + 3 2n - 1}{( 3 2) n}$

= $\frac{3 2n + 3 2n - 1}{3 2n}$

= $\frac{3 2n ( 1 + 3 - 1)}{3 2n}$

= 1 + 3^{- 1}

= 1 + $\frac{1}{3}$

= $\frac{4}{3}$

For more info please see

Exponents

Exponents Question 8 of 10

8. Simplify and choose the correct answer: $\frac{27 3 - 2n 9 n - 1}{81 2 - n}$

8. Simplify and choose the correct answer:

$\frac{27 3 - 2n 9 n - 1}{81 2 - n}$

\frac{1}{3}

B. 1

C. 3

D. None of the above

Correct Answer
Option A

Detailed Solution

Solution Details

Given $\frac{27 3 - 2n 9 n - 1}{81 2 - n}$

• $\frac{27 3 - 2n 9 n - 1}{81 2 - n}$

= $\frac{( 3 3) 3 - 2n ( 3 2) n - 1}{( 3 4) 2 - n}$

= $\frac{3 9 - 6n 3 2n - 2}{3 8 - 4n}$

= 3 ^{9 - 6n + 2n - 2 - 8 + 4n}

= 3 ^{- 1}

= $\frac{1}{3}$

For more info please see

Exponents

Exponents Question 9 of 10

9. Simplify and choose the correct answer: $\frac{5 n + 1 - 5 n + 2}{5 n + 1}$

9. Simplify and choose the correct answer:

$\frac{5 n + 1 - 5 n + 2}{5 n + 1}$

A. 4

B. - 4

C.0

D. None of the above

Correct Answer
Option B

Detailed Solution

Solution Details

Given $\frac{5 n + 1 - 5 n + 2}{5 n + 1}$

• $\frac{5 n + 1 - 5 n + 2}{5 n + 1}$

= $\frac{5 n + 1 ( 1 - 5 )}{5 n + 1}$

= 1 - 5

= - 4

For more info please see

Exponents

Exponents Question 10 of 10

10. Simplify and choose the correct answer: $\frac{22009 - 2 2011}{22010}$

10. Simplify and choose the correct answer:

$\frac{22009 - 2 2011}{22010}$

\frac{3}{2}

B. 1

C. -

\frac{3}{2}

D. None of the above

Correct Answer
Option C

Detailed Solution

Solution Details

Given $\frac{22009 - 2 2011}{22010}$

• $\frac{22009 - 2 2011}{22010}$

= $\frac{22009 ( 1 - 2 2)}{22009 ( 2 )}$

= $\frac{1 - 4}{2}$

= - $\frac{3}{2}$

For more info please see

Exponents

Quiz

Exponents and Surds

Exponents

Quiz Quidelines

Quiz

1. Simplify and choose the correct answer: ( a - 5 b - 2 ) 3

1. Simplify and choose the correct answer: ( a - 5 b - 2 ) 3

1. Simplify and choose the correct answer: ( a - 5 b - 2 ) 3

2. Simplify and choose the correct answer: x - 1 + y - 1

2. Simplify and choose the correct answer: x - 1 + y - 1

2. Simplify and choose the correct answer: x - 1 + y - 1

3. Simplify and choose the correct answer: 5 ( 2a 4 ) 3 (- 5a 3 ) 2 - 5a 6

3. Simplify and choose the correct answer: 5 ( 2a 4 ) 3 (- 5a 3 ) 2 - 5a 6

3. Simplify and choose the correct answer: 5 ( 2a 4 ) 3 (- 5a 3 ) 2 - 5a 6

4. Simplify and choose the correct answer: -3 ( ( - 2a 3 ) 2 + 9a 12 )

4. Simplify and choose the correct answer: -3 ( ( - 2a 3 ) 2 + 9a 12 )

4. Simplify and choose the correct answer: -3 ( ( - 2a 3 ) 2 + 9a 12 )

5. Simplify and choose the correct answer: ( x 4 ) n - 1 ( x 2y ) - 3n ( xy ) - 2n y - n

5. Simplify and choose the correct answer: ( x 4 ) n - 1 ( x 2y ) - 3n ( xy ) - 2n y - n

5. Simplify and choose the correct answer: ( x 4 ) n - 1 ( x 2y ) - 3n ( xy ) - 2n y - n

6. Simplify and choose the correct answer: 5 2n 9 3n - 3 15 2n 3 4n - 1

6. Simplify and choose the correct answer: 5 2n 9 3n - 3 15 2n 3 4n - 1

6. Simplify and choose the correct answer: 5 2n 9 3n - 3 15 2n 3 4n - 1

7. Simplify and choose the correct answer: 9 n + 3 2n - 1 9 n

7. Simplify and choose the correct answer: 9 n + 3 2n - 1 9 n

7. Simplify and choose the correct answer: 9 n + 3 2n - 1 9 n

8. Simplify and choose the correct answer: 27 3 - 2n 9 n - 1 81 2 - n

8. Simplify and choose the correct answer: 27 3 - 2n 9 n - 1 81 2 - n

8. Simplify and choose the correct answer: 27 3 - 2n 9 n - 1 81 2 - n

9. Simplify and choose the correct answer: 5 n + 1 - 5 n + 2 5 n + 1

9. Simplify and choose the correct answer: 5 n + 1 - 5 n + 2 5 n + 1

9. Simplify and choose the correct answer: 5 n + 1 - 5 n + 2 5 n + 1

10. Simplify and choose the correct answer: 2 2009 - 2 2011 2 2010

10. Simplify and choose the correct answer: 2 2009 - 2 2011 2 2010

10. Simplify and choose the correct answer: 2 2009 - 2 2011 2 2010

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Quiz Results

Solutions

1. Simplify and choose the correct answer: ( a - 5 b - 2 ) 3

1. Simplify and choose the correct answer: ( a - 5 b - 2 ) 3

1. Simplify and choose the correct answer: ( a - 5 b - 2 ) 3

Correct Answer Option B

Detailed Solution

Solution Details

Given ( a - 5 b - 2 ) 3

• ( a - 5 b - 2 ) 3 = a - 5 x 3 b - 2 x 3 = a - 15 b - 6 = b 6 a 15

2. Simplify and choose the correct answer: x - 1 + y - 1

2. Simplify and choose the correct answer: x - 1 + y - 1

2. Simplify and choose the correct answer: x - 1 + y - 1

Correct Answer Option C

Detailed Solution

Solution Details

Given x - 1 + y - 1

• x - 1 + y - 1 = 1 x + 1 y = y + x xy

3. Simplify and choose the correct answer: 5 ( 2a 4 ) 3 (- 5a 3 ) 2 - 5a 6

3. Simplify and choose the correct answer: 5 ( 2a 4 ) 3 (- 5a 3 ) 2 - 5a 6

3. Simplify and choose the correct answer: 5 ( 2a 4 ) 3 (- 5a 3 ) 2 - 5a 6

Correct Answer Option C

Detailed Solution

Solution Details

Given 5 ( 2a 4 ) 3 (- 5a 3 ) 2 - 5a 6

• 5 ( 2a 4 ) 3 (- 5a 3 ) 2 - 5a 6 = 5 ( 2 3) ( a 4 x 3 ) (- 5 2) ( a 3 x 2 ) - 5a 6 = 5 ( 8a 12 ) 25a 6 - 5a 6 = 40a 12 20a 6 = 2a 6

4. Simplify and choose the correct answer: -3 ( ( - 2a 3 ) 2 + 9a 12 )

4. Simplify and choose the correct answer: -3 ( ( - 2a 3 ) 2 + 9a 12 )

4. Simplify and choose the correct answer: -3 ( ( - 2a 3 ) 2 + 9a 12 )

Correct Answer Option A

Detailed Solution

Solution Details

Given -3 ( ( - 2a 3 ) 2 + 9a 12 )

• - 3 ( ( - 2a 3 ) 2 + 9a 12 ) = - 3 ( 4a 6 + 3a 6 ) = - 3 ( 7a 6 ) = - 21a 6

5. Simplify and choose the correct answer: ( x 4 ) n - 1 ( x 2y ) - 3n ( xy ) - 2n y - n

5. Simplify and choose the correct answer: ( x 4 ) n - 1 ( x 2y ) - 3n ( xy ) - 2n y - n

5. Simplify and choose the correct answer: ( x 4 ) n - 1 ( x 2y ) - 3n ( xy ) - 2n y - n

Correct Answer Option A

Detailed Solution

Solution Details

Given ( x 4 ) n - 1 ( x 2y ) - 3n ( xy ) - 2n y - n

• ( x 4 ) n - 1 ( x 2y ) - 3n ( xy ) - 2n y - n = ( x 4n - 4 ) ( x - 6n ) ( y - 3n ) ( x - 2n ) ( y - 2n ) y - n = x 4n - 4 - 6n + 2n y - 3n + 2n + n = x - 4 y 0 = x - 4 = 1 x 4

6. Simplify and choose the correct answer: 5 2n 9 3n - 3 15 2n 3 4n - 1

6. Simplify and choose the correct answer: 5 2n 9 3n - 3 15 2n 3 4n - 1

1. Simplify and choose the correct answer: ( $\frac{a - 5}{b - 2}$ )³

1. Simplify and choose the correct answer: ( $\frac{a - 5}{b - 2}$ )³

1. Simplify and choose the correct answer:

( $\frac{a - 5}{b - 2}$ )³

2. Simplify and choose the correct answer: x^{- 1} + y^{- 1}

2. Simplify and choose the correct answer: x^{- 1} + y^{- 1}

2. Simplify and choose the correct answer:

x^{- 1} + y^{- 1}

3. Simplify and choose the correct answer: $\frac{5 ( 2a 4) 3}{(- 5a 3) 2 - 5a 6}$

3. Simplify and choose the correct answer: $\frac{5 ( 2a 4) 3}{(- 5a 3) 2 - 5a 6}$

3. Simplify and choose the correct answer:

$\frac{5 ( 2a 4) 3}{(- 5a 3) 2 - 5a 6}$

4. Simplify and choose the correct answer: -3 ( ( - 2a³ ) ² + $\sqrt[]{9a 12}$ )

4. Simplify and choose the correct answer: -3 ( ( - 2a³ ) ² + $\sqrt[]{9a 12}$ )

4. Simplify and choose the correct answer:

-3 ( ( - 2a³ ) ² + $\sqrt[]{9a 12}$ )

5. Simplify and choose the correct answer: $\frac{( x 4) n - 1 ( x 2 y ) - 3n}{( xy ) - 2n y - n}$

5. Simplify and choose the correct answer: $\frac{( x 4) n - 1 ( x 2 y ) - 3n}{( xy ) - 2n y - n}$

5. Simplify and choose the correct answer:

$\frac{( x 4) n - 1 ( x 2 y ) - 3n}{( xy ) - 2n y - n}$

6. Simplify and choose the correct answer: $\frac{5 2n 9 3n - 3}{15 2n 3 4n - 1}$

6. Simplify and choose the correct answer: $\frac{5 2n 9 3n - 3}{15 2n 3 4n - 1}$

6. Simplify and choose the correct answer:

$\frac{5 2n 9 3n - 3}{15 2n 3 4n - 1}$

7. Simplify and choose the correct answer: $\frac{9 n + 3 2n - 1}{9 n}$

7. Simplify and choose the correct answer: $\frac{9 n + 3 2n - 1}{9 n}$

7. Simplify and choose the correct answer:

$\frac{9 n + 3 2n - 1}{9 n}$

8. Simplify and choose the correct answer: $\frac{27 3 - 2n 9 n - 1}{81 2 - n}$

8. Simplify and choose the correct answer: $\frac{27 3 - 2n 9 n - 1}{81 2 - n}$

8. Simplify and choose the correct answer:

$\frac{27 3 - 2n 9 n - 1}{81 2 - n}$

9. Simplify and choose the correct answer: $\frac{5 n + 1 - 5 n + 2}{5 n + 1}$

9. Simplify and choose the correct answer: $\frac{5 n + 1 - 5 n + 2}{5 n + 1}$

9. Simplify and choose the correct answer:

$\frac{5 n + 1 - 5 n + 2}{5 n + 1}$

10. Simplify and choose the correct answer: $\frac{22009 - 2 2011}{22010}$

10. Simplify and choose the correct answer: $\frac{22009 - 2 2011}{22010}$

10. Simplify and choose the correct answer:

$\frac{22009 - 2 2011}{22010}$

1. Simplify and choose the correct answer: ( $\frac{a - 5}{b - 2}$ )³

1. Simplify and choose the correct answer: ( $\frac{a - 5}{b - 2}$ )³

1. Simplify and choose the correct answer:

( $\frac{a - 5}{b - 2}$ )³

Correct Answer
Option B

Given ( $\frac{a - 5}{b - 2}$ )³

• ( $\frac{a - 5}{b - 2}$ )³

= $\frac{a - 5 x 3}{b - 2 x 3}$

= $\frac{a - 15}{b - 6}$

= $\frac{b 6}{a 15}$

2. Simplify and choose the correct answer: x^{- 1} + y^{- 1}

2. Simplify and choose the correct answer: x^{- 1} + y^{- 1}

2. Simplify and choose the correct answer:

x^{- 1} + y^{- 1}

Correct Answer
Option C

Given x^{- 1} + y^{- 1}

• x^{- 1} + y^{- 1}

= $\frac{1}{x}$ + $\frac{1}{y}$

= $\frac{y + x}{xy}$

3. Simplify and choose the correct answer: $\frac{5 ( 2a 4) 3}{(- 5a 3) 2 - 5a 6}$

3. Simplify and choose the correct answer: $\frac{5 ( 2a 4) 3}{(- 5a 3) 2 - 5a 6}$

3. Simplify and choose the correct answer:

$\frac{5 ( 2a 4) 3}{(- 5a 3) 2 - 5a 6}$

Correct Answer
Option C

Given $\frac{5 ( 2a 4) 3}{(- 5a 3) 2 - 5a 6}$

• $\frac{5 ( 2a 4) 3}{(- 5a 3) 2 - 5a 6}$

= $\frac{5 ( 2 3) ( a 4 x 3)}{(- 5 2) ( a 3 x 2) - 5a 6}$

= $\frac{5 ( 8a 12)}{25a 6 - 5a 6}$

= $\frac{40a 12}{20a 6}$

= 2a⁶

4. Simplify and choose the correct answer: -3 ( ( - 2a³ ) ² + $\sqrt[]{9a 12}$ )

4. Simplify and choose the correct answer: -3 ( ( - 2a³ ) ² + $\sqrt[]{9a 12}$ )

4. Simplify and choose the correct answer:

-3 ( ( - 2a³ ) ² + $\sqrt[]{9a 12}$ )

Correct Answer
Option A

Given -3 ( ( - 2a³ ) ² + $\sqrt[]{9a 12}$ )

• - 3 ( ( - 2a³ ) ² + $\sqrt[]{9a 12}$ )

= - 3 ( 4a⁶ + 3a⁶ )

= - 3 ( 7a⁶ )

= - 21a⁶

5. Simplify and choose the correct answer: $\frac{( x 4) n - 1 ( x 2 y ) - 3n}{( xy ) - 2n y - n}$

5. Simplify and choose the correct answer: $\frac{( x 4) n - 1 ( x 2 y ) - 3n}{( xy ) - 2n y - n}$

5. Simplify and choose the correct answer:

$\frac{( x 4) n - 1 ( x 2 y ) - 3n}{( xy ) - 2n y - n}$

Correct Answer
Option A

Given $\frac{( x 4) n - 1 ( x 2 y ) - 3n}{( xy ) - 2n y - n}$

• $\frac{( x 4) n - 1 ( x 2 y ) - 3n}{( xy ) - 2n y - n}$

= $\frac{( x 4n - 4) ( x - 6n) ( y - 3n)}{( x - 2n) ( y - 2n) y - n}$

= x^{4n - 4 - 6n + 2n} y^{- 3n + 2n + n}

= x ^{- 4} y⁰

= x ^{- 4}

= $\frac{1}{x 4}$

6. Simplify and choose the correct answer: $\frac{5 2n 9 3n - 3}{15 2n 3 4n - 1}$

6. Simplify and choose the correct answer: $\frac{5 2n 9 3n - 3}{15 2n 3 4n - 1}$

6. Simplify and choose the correct answer:

$\frac{5 2n 9 3n - 3}{15 2n 3 4n - 1}$

Correct Answer
Option C

Given $\frac{5 2n 9 3n - 3}{15 2n 3 4n - 1}$

• $\frac{5 2n 9 3n - 3}{15 2n 3 4n - 1}$

= $\frac{5 2n ( 3 2) 3n - 3}{( 5 x 3 ) 2n 3 4n - 1}$

= $\frac{5 2n 3 6n - 6}{5 2n 3 2n 3 4n - 1}$

= 5^{2n - 2n} 3 ^{6n - 6 - 2n - 4n + 1}

= 5⁰ 3 ^{- 5}

= $\frac{1}{35}$

= $\frac{1}{243}$

7. Simplify and choose the correct answer: $\frac{9 n + 3 2n - 1}{9 n}$

7. Simplify and choose the correct answer: $\frac{9 n + 3 2n - 1}{9 n}$

7. Simplify and choose the correct answer:

$\frac{9 n + 3 2n - 1}{9 n}$

Correct Answer
Option B

Given $\frac{9 n + 3 2n - 1}{9 n}$

• $\frac{9 n + 3 2n - 1}{9 n}$

= $\frac{( 3 2) n + 3 2n - 1}{( 3 2) n}$

= $\frac{3 2n + 3 2n - 1}{3 2n}$

= $\frac{3 2n ( 1 + 3 - 1)}{3 2n}$

= 1 + 3^{- 1}

= 1 + $\frac{1}{3}$

= $\frac{4}{3}$

8. Simplify and choose the correct answer: $\frac{27 3 - 2n 9 n - 1}{81 2 - n}$

8. Simplify and choose the correct answer: $\frac{27 3 - 2n 9 n - 1}{81 2 - n}$

8. Simplify and choose the correct answer:

$\frac{27 3 - 2n 9 n - 1}{81 2 - n}$

Correct Answer
Option A

Given $\frac{27 3 - 2n 9 n - 1}{81 2 - n}$

• $\frac{27 3 - 2n 9 n - 1}{81 2 - n}$

= $\frac{( 3 3) 3 - 2n ( 3 2) n - 1}{( 3 4) 2 - n}$

= $\frac{3 9 - 6n 3 2n - 2}{3 8 - 4n}$

= 3 ^{9 - 6n + 2n - 2 - 8 + 4n}

= 3 ^{- 1}

= $\frac{1}{3}$

9. Simplify and choose the correct answer: $\frac{5 n + 1 - 5 n + 2}{5 n + 1}$

9. Simplify and choose the correct answer: $\frac{5 n + 1 - 5 n + 2}{5 n + 1}$