Simplify (15h^-4k^15)/(5h^4k^5)

$\frac{15 h^{- 4} k^{15}}{5 h^{4} k^{5}}$

Move $h^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{15 k^{15}}{5 h^{4} k^{5} h^{4}}$

Multiply $h^{4}$ by $h^{4}$ by adding the exponents.

Move $h^{4}$ .

$\frac{15 k^{15}}{5 (h^{4} h^{4}) k^{5}}$

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

$\frac{15 k^{15}}{5 h^{4 + 4} k^{5}}$

Add $4$ and $4$ .

$\frac{15 k^{15}}{5 h^{8} k^{5}}$

Cancel the common factor of $15$ and $5$ .

Factor $5$ out of $15 k^{15}$ .

$\frac{5 (3 k^{15})}{5 h^{8} k^{5}}$

Cancel the common factors.

Factor $5$ out of $5 h^{8} k^{5}$ .

$\frac{5 (3 k^{15})}{5 (h^{8} k^{5})}$

Cancel the common factor.

$\frac{5 (3 k^{15})}{5 (h^{8} k^{5})}$

Rewrite the expression.

$\frac{3 k^{15}}{h^{8} k^{5}}$

Cancel the common factor of $k^{15}$ and $k^{5}$ .

Factor $k^{5}$ out of $3 k^{15}$ .

$\frac{k^{5} (3 k^{10})}{h^{8} k^{5}}$

Cancel the common factors.

Factor $k^{5}$ out of $h^{8} k^{5}$ .

$\frac{k^{5} (3 k^{10})}{k^{5} h^{8}}$

Cancel the common factor.

$\frac{k^{5} (3 k^{10})}{k^{5} h^{8}}$

Rewrite the expression.

$\frac{3 k^{10}}{h^{8}}$