Simplify -(10h^6)/((2h^-3)^5)

$- \frac{10 h^{6}}{{(2 h^{- 3})}^{5}}$

Simplify the denominator.

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

$- \frac{10 h^{6}}{2^{5} {(h^{- 3})}^{5}}$

Raise $2$ to the power of $5$ .

$- \frac{10 h^{6}}{32 {(h^{- 3})}^{5}}$

Multiply the exponents in ${(h^{- 3})}^{5}$ .

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

$- \frac{10 h^{6}}{32 h^{- 3 \cdot 5}}$

Multiply $- 3$ by $5$ .

$- \frac{10 h^{6}}{32 h^{- 15}}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$- \frac{10 h^{6}}{32 \frac{1}{h^{15}}}$

Combine $32$ and $\frac{1}{h^{15}}$ .

$- \frac{10 h^{6}}{\frac{32}{h^{15}}}$

Multiply the numerator by the reciprocal of the denominator.

$- (10 h^{6} \frac{h^{15}}{32})$

Cancel the common factor of $2$ .

Factor $2$ out of $10 h^{6}$ .

$- (2 (5 h^{6}) \frac{h^{15}}{32})$

Factor $2$ out of $32$ .

$- (2 (5 h^{6}) \frac{h^{15}}{2 (16)})$

Cancel the common factor.

$- (2 (5 h^{6}) \frac{h^{15}}{2 \cdot 16})$

Rewrite the expression.

$- (5 h^{6} \frac{h^{15}}{16})$

Combine $5$ and $\frac{h^{15}}{16}$ .

$- (h^{6} \frac{5 h^{15}}{16})$

Combine $h^{6}$ and $\frac{5 h^{15}}{16}$ .

$- \frac{h^{6} (5 h^{15})}{16}$

Multiply $h^{6}$ by $h^{15}$ by adding the exponents.

Move $h^{15}$ .

$- \frac{h^{15} h^{6} \cdot 5}{16}$

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

$- \frac{h^{15 + 6} \cdot 5}{16}$

Add $15$ and $6$ .

$- \frac{h^{21} \cdot 5}{16}$

Move $5$ to the left of $h^{21}$ .

$- \frac{5 h^{21}}{16}$