Simplify ((-4d^4)^2)/(-5d^-10)

$\frac{{(- 4 d^{4})}^{2}}{- 5 d^{- 10}}$

Step 1

Move $d^{- 10}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{{(- 4 d^{4})}^{2} d^{10}}{- 5}$

Step 2

Simplify the numerator.

Apply the product rule to $- 4 d^{4}$ .

$\frac{{(- 4)}^{2} {(d^{4})}^{2} d^{10}}{- 5}$

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

$\frac{16 {(d^{4})}^{2} d^{10}}{- 5}$

Multiply the exponents in ${(d^{4})}^{2}$ .

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

$\frac{16 d^{4 \cdot 2} d^{10}}{- 5}$

Multiply $4$ by $2$ .

$\frac{16 d^{8} d^{10}}{- 5}$

Multiply $d^{8}$ by $d^{10}$ by adding the exponents.

Move $d^{10}$ .

$\frac{16 (d^{10} d^{8})}{- 5}$

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

$\frac{16 d^{10 + 8}}{- 5}$

Add $10$ and $8$ .

$\frac{16 d^{18}}{- 5}$

Step 3

Move the negative in front of the fraction.

$- \frac{16 d^{18}}{5}$