Question

Rational Exponents Practice
Complete this assessment to review what you’ve learned. It will not count toward your grade.
2 of 52 of 5 Items


Question
Rewrite the expression as a product of identical factors to simplify 12523
. Submit your answer in simplified form. (1 point)

Answer 1

To simplify the expression \( 125^{\frac{2}{3}} \), we can rewrite it as a product of identical factors.

First, recognize that \( 125 \) can be expressed as a power of \( 5 \):
\[
125 = 5^3
\]

Now we can rewrite the expression:
\[
125^{\frac{2}{3}} = (5^3)^{\frac{2}{3}}
\]

Using the power of a power property \((a^m)^n = a^{m \cdot n}\), we multiply the exponents:
\[
(5^3)^{\frac{2}{3}} = 5^{3 \cdot \frac{2}{3}} = 5^2
\]

Now, we can simplify \( 5^2 \):
\[
5^2 = 25
\]

Thus, the simplified form of \( 125^{\frac{2}{3}} \) is:
\[
\boxed{25}
\]