Question

rational exponents practice
complete this assessment to review what youve learned. it will not count toward your grade.
rewrite the expression as a product of identical factors to simplify ( 125^{\frac{2}{3}} ). submit your answer in simplified form. (1 point)

check answer remaining attempts: 3

Explanation:

Step1: Recall the formula for rational exponents

The formula for a rational exponent \( a^{\frac{m}{n}} \) is \( \sqrt[n]{a^m} \) or \( (\sqrt[n]{a})^m \). For \( 125^{\frac{2}{3}} \), we can use \( (\sqrt[3]{125})^2 \) since the denominator of the exponent is the root and the numerator is the power.

Step2: Find the cube root of 125

We know that \( 5\times5\times5 = 125 \), so \( \sqrt[3]{125}=5 \).

Step3: Square the result

Now we square 5: \( 5^2 = 25 \).

Answer:

25