Simplify (10n)/(2(n^-3)^4)

$\frac{10 n}{2 {(n^{- 3})}^{4}}$

Step 1

Cancel the common factor of $10$ and $2$ .

Factor $2$ out of $10 n$ .

$\frac{2 (5 n)}{2 {(n^{- 3})}^{4}}$

Cancel the common factors.

Factor $2$ out of $2 {(n^{- 3})}^{4}$ .

$\frac{2 (5 n)}{2 ({(n^{- 3})}^{4})}$

Cancel the common factor.

$\frac{2 (5 n)}{2 {(n^{- 3})}^{4}}$

Rewrite the expression.

$\frac{5 n}{{(n^{- 3})}^{4}}$

Step 2

Simplify the denominator.

Multiply the exponents in ${(n^{- 3})}^{4}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{5 n}{n^{- 3 \cdot 4}}$

Multiply $- 3$ by $4$ .

$\frac{5 n}{n^{- 12}}$

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

$\frac{5 n}{\frac{1}{n^{12}}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$5 n \cdot n^{12}$

Step 4

Multiply $n$ by $n^{12}$ by adding the exponents.

Move $n^{12}$ .

$5 (n^{12} n)$

Multiply $n^{12}$ by $n$ .

Raise $n$ to the power of $1$ .

$5 (n^{12} n^{1})$

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

$5 n^{12 + 1}$

Add $12$ and $1$ .

$5 n^{13}$