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

Identify base and exponent: Identify the base and the exponent in the expression (a^(3))^(6). 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). (a^(3))^(6) = a^(3*6)Multiply exponents: Multiply the exponents to simplify the expression. 3 * 6 = 18 So, (a^(3))^(6) = a^(18)Check answer choices: Check the answer choices to see which one matches the simplified expression. The correct answer is B. a^(18).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

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

Home

Math Problems

Algebra 2

Evaluate rational exponents

Full solution

Q. Which expression is equivalent to

\newline

(a^{3})^{6}

\newline

a^{729}

\newline

a^{18}

\newline

a^9

\newline

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. $a^{18}$ .