Question

evaluate.
$16^{\frac{1}{4}} = \square$
$125^{\frac{1}{3}} = \square$

Explanation:

Step1: Rewrite base as power of 2

$16 = 2^4$, so $16^{\frac{1}{4}} = (2^4)^{\frac{1}{4}}$

Step2: Apply exponent power rule

$(2^4)^{\frac{1}{4}} = 2^{4 \times \frac{1}{4}} = 2^1 = 2$

Step3: Rewrite base as power of 5

$125 = 5^3$, so $125^{\frac{1}{3}} = (5^3)^{\frac{1}{3}}$

Step4: Apply exponent power rule

$(5^3)^{\frac{1}{3}} = 5^{3 \times \frac{1}{3}} = 5^1 = 5$

Answer:

$16^{\frac{1}{4}} = 2$
$125^{\frac{1}{3}} = 5$