Question

Using the Power Rule of Exponents, what is an equivalent form of ((2/3)^8)^2
?(1 point)
Responses

(2/3)^6
left parenthesis Start Fraction 2 over 3 End Fraction right parenthesis superscript 6 baseline

(2/3)^4
left parenthesis Start Fraction 2 over 3 End Fraction right parenthesis superscript 4 baseline

(2/3)^16
left parenthesis Start Fraction 2 over 3 End Fraction right parenthesis superscript 16 baseline

(2/3)^10

Answer 1

To simplify \(((2/3)^8)^2\) using the Power Rule of Exponents, you multiply the exponents. The Power Rule states that \((a^m)^n = a^{m \times n}\).

Applying the rule here:

\[
((2/3)^8)^2 = (2/3)^{8 \times 2} = (2/3)^{16}
\]

So the equivalent form is:

\((2/3)^{16}\)

Thus, the correct response is:

\((2/3)^{16}\)