Simplify (10h^10)/((-5h^5q)^3)

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

Step 1

Simplify the denominator.

Apply the product rule to $- 5 h^{5} q$ .

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

Apply the product rule to $- 5 h^{5}$ .

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

Raise $- 5$ to the power of $3$ .

$\frac{10 h^{10}}{- 125 {(h^{5})}^{3} q^{3}}$

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

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

$\frac{10 h^{10}}{- 125 h^{5 \cdot 3} q^{3}}$

Multiply $5$ by $3$ .

$\frac{10 h^{10}}{- 125 h^{15} q^{3}}$

Step 2

Reduce the expression by cancelling the common factors.

Cancel the common factor of $10$ and $- 125$ .

Factor $5$ out of $10 h^{10}$ .

$\frac{5 (2 h^{10})}{- 125 h^{15} q^{3}}$

Cancel the common factors.

Factor $5$ out of $- 125 h^{15} q^{3}$ .

$\frac{5 (2 h^{10})}{5 (- 25 h^{15} q^{3})}$

Cancel the common factor.

$\frac{5 (2 h^{10})}{5 (- 25 h^{15} q^{3})}$

Rewrite the expression.

$\frac{2 h^{10}}{- 25 h^{15} q^{3}}$

Cancel the common factor of $h^{10}$ and $h^{15}$ .

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

$\frac{h^{10} \cdot 2}{- 25 h^{15} q^{3}}$

Cancel the common factors.

Factor $h^{10}$ out of $- 25 h^{15} q^{3}$ .

$\frac{h^{10} \cdot 2}{h^{10} (- 25 h^{5} q^{3})}$

Cancel the common factor.

$\frac{h^{10} \cdot 2}{h^{10} (- 25 h^{5} q^{3})}$

Rewrite the expression.

$\frac{2}{- 25 h^{5} q^{3}}$

Move the negative in front of the fraction.

$- \frac{2}{25 h^{5} q^{3}}$