Simplify square root of 16a^8b^-2

$\sqrt{16 a^{8} b^{- 2}}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\sqrt{16 a^{8} \frac{1}{b^{2}}}$

Step 2

Combine exponents.

Combine $16$ and $\frac{1}{b^{2}}$ .

$\sqrt{a^{8} \frac{16}{b^{2}}}$

Combine $a^{8}$ and $\frac{16}{b^{2}}$ .

$\sqrt{\frac{a^{8} \cdot 16}{b^{2}}}$

Step 3

Move $16$ to the left of $a^{8}$ .

$\sqrt{\frac{16 \cdot a^{8}}{b^{2}}}$

Step 4

Rewrite $16 a^{8}$ as ${(4 a^{4})}^{2}$ .

$\sqrt{\frac{{(4 a^{4})}^{2}}{b^{2}}}$

Step 5

Rewrite $\frac{{(4 a^{4})}^{2}}{b^{2}}$ as ${(\frac{4 a^{4}}{b})}^{2}$ .

$\sqrt{{(\frac{4 a^{4}}{b})}^{2}}$

Step 6

Pull terms out from under the radical, assuming positive real numbers.

$\frac{4 a^{4}}{b}$