Simplify ((-2s^3)^4)/(5s^-1)

$\frac{{(- 2 s^{3})}^{4}}{5 s^{- 1}}$

Step 1

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

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

Step 2

Simplify the numerator.

Apply the product rule to $- 2 s^{3}$ .

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

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

$\frac{16 {(s^{3})}^{4} s}{5}$

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

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

$\frac{16 s^{3 \cdot 4} s}{5}$

Multiply $3$ by $4$ .

$\frac{16 s^{12} s}{5}$

Combine exponents.

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

$\frac{16 (s^{1} s^{12})}{5}$

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

$\frac{16 s^{1 + 12}}{5}$

Add $1$ and $12$ .

$\frac{16 s^{13}}{5}$