Simplify 12 root of 1/(n^-8*n^-7)

$\sqrt[12]{\frac{1}{n^{- 8} \cdot n^{- 7}}}$

Step 1

Reduce the expression by cancelling the common factors.

Move $n^{- 8}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\sqrt[12]{\frac{n^{8}}{n^{- 7}}}$

Move $n^{- 7}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\sqrt[12]{n^{8} n^{7}}$

Multiply $n^{8}$ by $n^{7}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sqrt[12]{n^{8 + 7}}$

Add $8$ and $7$ .

$\sqrt[12]{n^{15}}$

Step 2

Factor out $n^{12}$ .

$\sqrt[12]{n^{12} n^{3}}$

Step 3

Pull terms out from under the radical.

$n \sqrt[12]{n^{3}}$

Step 4

Rewrite $\sqrt[12]{n^{3}}$ as $\sqrt[4]{\sqrt[3]{n^{3}}}$ .

$n \sqrt[4]{\sqrt[3]{n^{3}}}$

Step 5

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

$n \sqrt[4]{n}$