Question

select the equivalent expression.$sqrt16{\frac{a^{-6}}{a^{2}}}$answer$\bigcirc a^{-2}$$\bigcirc a^{\frac{1}{2}}$$\bigcirc a^{2}$$\bigcirc a^{-\frac{1}{2}}$

Explanation:

Step1: Simplify exponents inside root

When dividing like bases, subtract exponents: $a^{-6 - 2} = a^{-8}$
So the expression becomes $\sqrt[16]{a^{-8}}$

Step2: Rewrite root as rational exponent

A 16th root is an exponent of $\frac{1}{16}$: $(a^{-8})^{\frac{1}{16}}$

Step3: Multiply exponents

Multiply the exponents: $-8 \times \frac{1}{16} = -\frac{1}{2}$
So we get $a^{-\frac{1}{2}}$

Answer:

$a^{-\frac{1}{2}}$ (the bottom-right option)