Rational Exponents Practice

Question

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: \[ \boxed{25} \]