Simplify ((4n)^2)/(-4n^-5)

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

Step 1

Move $n^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 2

Simplify the numerator.

Apply the product rule to $4 n$ .

$\frac{4^{2} n^{2} n^{5}}{- 4}$

Multiply $n^{2}$ by $n^{5}$ by adding the exponents.

Move $n^{5}$ .

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

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

$\frac{4^{2} n^{5 + 2}}{- 4}$

Add $5$ and $2$ .

$\frac{4^{2} n^{7}}{- 4}$

Raise $4$ to the power of $2$ .

$\frac{16 n^{7}}{- 4}$

Step 3

Reduce the expression by cancelling the common factors.

Cancel the common factor of $16$ and $- 4$ .

Factor $4$ out of $16 n^{7}$ .

$\frac{4 (4 n^{7})}{- 4}$

Move the negative one from the denominator of $\frac{4 n^{7}}{- 1}$ .

$- 1 \cdot (4 n^{7})$

Simplify the expression.

Rewrite $- 1 \cdot (4 n^{7})$ as $- (4 n^{7})$ .

$- (4 n^{7})$

Multiply $4$ by $- 1$ .

$- 4 n^{7}$