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

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

Move $s^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Simplify the numerator.

Apply the product rule to $4 s^{4}$ .

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

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

$\frac{256 {(s^{4})}^{4} s^{3}}{2}$

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

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

$\frac{256 s^{4 \cdot 4} s^{3}}{2}$

Multiply $4$ by $4$ .

$\frac{256 s^{16} s^{3}}{2}$

Multiply $s^{16}$ by $s^{3}$ by adding the exponents.

Move $s^{3}$ .

$\frac{256 (s^{3} s^{16})}{2}$

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

$\frac{256 s^{3 + 16}}{2}$

Add $3$ and $16$ .

$\frac{256 s^{19}}{2}$

Cancel the common factor of $256$ and $2$ .

Factor $2$ out of $256 s^{19}$ .

$\frac{2 (128 s^{19})}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$\frac{2 (128 s^{19})}{2 (1)}$

Cancel the common factor.

$\frac{2 (128 s^{19})}{2 \cdot 1}$

Rewrite the expression.

$\frac{128 s^{19}}{1}$

Divide $128 s^{19}$ by $1$ .

$128 s^{19}$