Question

1. write $7^{-\frac{2}{3}}$ without exponents.

type the answer in the box below.
$7^{-\frac{2}{3}} = \boxed{}$

1. write $\sqrt4{11^5}$ in the form $a^b$ without radicals.

type the answer in the box below.
$\sqrt4{11^5} = \boxed{}$

Explanation:

Step1: Handle negative exponent

$7^{-\frac{2}{3}} = \frac{1}{7^{\frac{2}{3}}}$

Step2: Convert to radical form

$\frac{1}{7^{\frac{2}{3}}} = \frac{1}{\sqrt[3]{7^2}} = \frac{1}{\sqrt[3]{49}}$

Step3: Convert radical to exponent

$\sqrt[4]{11^5} = 11^{\frac{5}{4}}$

Answer:

1. $\frac{1}{\sqrt[3]{49}}$
2. $11^{\frac{5}{4}}$