Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Which expression is equivalent to $\newline$ $(a^{3})^{6}$ ? $\newline$ A. $a^{729}$ $\newline$ B. $a^{18}$ $\newline$ C. $a^9$ $\newline$ D. $a^2$

View step-by-step help

View step-by-step help

Evaluate rational exponents

Full solution

Q. Which expression is equivalent to

\newline

(a^{3})^{6}

?

\newline

A.

a^{729}

\newline

B.

a^{18}

\newline

C.

a^9

\newline

D.

a^2

Identify base and exponent: Identify the base and the exponent in the expression $(a^{3})^{6}$ . $\newline$ In $(a^{3})^{6}$ , the base is $a^{3}$ , and the outer exponent is $6$ .
Apply power of power rule: Apply the power of a power rule, which states that $(a^m)^n = a^{m*n}$ . $\newline$ $(a^{3})^{6} = a^{3*6}$
Multiply exponents: Multiply the exponents to simplify the expression. $\newline$ $3 \times 6 = 18$ $\newline$ So, $(a^{3})^{6} = a^{18}$
Check answer choices: Check the answer choices to see which one matches the simplified expression. $\newline$ The correct answer is B. $a^{18}$ .

More problems from Evaluate rational exponents

Question

\newline

81^{\frac{1}{2}}

\newline

Posted 9 months ago

Question

\newline

(-32)^{1/5}

\newline

Posted 9 months ago

Question

Simplify. Assume all variables are positive.

\newline

\frac{w^{\frac{4}{3}}}{w^{\frac{7}{3}}}

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

Posted 5 months ago

Question

Simplify. Assume all variables are positive.

\newline

(2r^{\frac{1}{3}})^8

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

Posted 5 months ago

Question

Simplify. Assume all variables are positive.

\newline

v^{\frac{7}{4}} \cdot v^{\frac{9}{4}}

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

\newline

Posted 5 months ago

Question

\newline

1^{\frac{1}{4}} \cdot 1^{\frac{1}{4}}

\newline

Posted 5 months ago

Question

\newline

32^{(-1/5)}

Posted 7 months ago

Question

Simplify. Assume all variables are positive.

\newline

\frac{w^{\frac{3}{2}}}{w^{\frac{5}{2}}}

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

\newline

Posted 9 months ago

Question

Simplify. Assume all variables are positive.

\newline

(27x)^{\frac{2}{3}}

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

Posted 8 months ago

Question

Simplify. Assume all variables are positive.

\newline

\frac{x^{\frac{1}{4}}}{x^{\frac{11}{4}}}

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

\newline

Posted 7 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant