# How do you simplify n^6 * (n^-2)^5?

Nov 4, 2015

${n}^{6} \cdot {\left({n}^{-} 2\right)}^{5} = \frac{1}{n} ^ 4$

#### Explanation:

${n}^{6} \cdot {\left({n}^{-} 2\right)}^{5}$

Simplify ${\left({n}^{-} 2\right)}^{5}$ by applying the exponent rule ${\left({a}^{m}\right)}^{n} = {a}^{m \cdot n}$.

${n}^{6} \cdot {n}^{- 2 \cdot 5} =$

${n}^{6} \cdot {n}^{-} 10$

Simplify by applying the exponent rule ${a}^{m} \cdot {a}^{n} = {a}^{m + n}$.

${n}^{6} \cdot {n}^{-} 10 =$

${n}^{6 \pm 10} =$

${n}^{-} 4$

Apply the exponent rule ${a}^{- m} = \frac{1}{a} ^ m$.

${n}^{-} 4 = \frac{1}{n} ^ 4$

Nov 4, 2015

$\frac{1}{n} ^ 4$

#### Explanation:

${n}^{6} \cdot \left({n}^{- 2 \cdot 5}\right) = {n}^{6} \cdot {n}^{- 10} = {n}^{6 + \left(- 10\right)} = {n}^{- 4} = \frac{1}{n} ^ 4$