Question

An expression is shown.
(3/4)^2 (3/4)^5











Which of the following is equivalent to the expression shown?

Responses
A





the fraction with numerator 3 to the 7th power and denominator 4 to the 7th power
B





the fraction with numerator 3 to the 10th power and denominator 4 to the 10th power
C





the fraction with numerator 3 to the 7th power and denominator 4
D

Answer 1

To simplify the expression \((3/4)^2 \cdot (3/4)^5\), you can apply the property of exponents that states \(a^m \cdot a^n = a^{m+n}\).

1. Combine the exponents:
\[
(3/4)^2 \cdot (3/4)^5 = (3/4)^{2+5} = (3/4)^7
\]

2. Rewrite \((3/4)^7\) in fraction form:
\[
(3/4)^7 = \frac{3^7}{4^7}
\]

Thus, the expression is equivalent to the fraction with numerator \(3^7\) and denominator \(4^7\).

Comparing this result with the provided options:

A. the fraction with numerator \(3^7\) and denominator \(4^7\) ✔️

B. the fraction with numerator \(3^{10}\) and denominator \(4^{10}\)

C. the fraction with numerator \(3^7\) and denominator \(4\)

D. (not provided)

The correct answer is **A**.