Write the Fraction in Simplest Form ((4h^4)^4)/(4h^-8)

$\frac{{(4 h^{4})}^{4}}{4 h^{- 8}}$

Move $h^{- 8}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{{(4 h^{4})}^{4} h^{8}}{4}$

Simplify the numerator.

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

$\frac{4^{4} {(h^{4})}^{4} h^{8}}{4}$

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

$\frac{256 {(h^{4})}^{4} h^{8}}{4}$

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

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

$\frac{256 h^{4 \cdot 4} h^{8}}{4}$

Multiply $4$ by $4$ .

$\frac{256 h^{16} h^{8}}{4}$

Multiply $h^{16}$ by $h^{8}$ by adding the exponents.

Move $h^{8}$ .

$\frac{256 (h^{8} h^{16})}{4}$

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

$\frac{256 h^{8 + 16}}{4}$

Add $8$ and $16$ .

$\frac{256 h^{24}}{4}$

Cancel the common factor of $256$ and $4$ .

Factor $4$ out of $256 h^{24}$ .

$\frac{4 (64 h^{24})}{4}$

Cancel the common factors.

Factor $4$ out of $4$ .

$\frac{4 (64 h^{24})}{4 (1)}$

Cancel the common factor.

$\frac{4 (64 h^{24})}{4 \cdot 1}$

Rewrite the expression.

$\frac{64 h^{24}}{1}$

Divide $64 h^{24}$ by $1$ .

$64 h^{24}$