Simplify (-3hk^-6)/(-9h^-7j^6k^0)

$\frac{- 3 h k^{- 6}}{- 9 h^{- 7} j^{6} k^{0}}$

Step 1

Move $k^{- 6}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{- 3 h}{- 9 h^{- 7} j^{6} k^{0} k^{6}}$

Step 2

Multiply $k^{0}$ by $k^{6}$ by adding the exponents.

Move $k^{6}$ .

$\frac{- 3 h}{- 9 h^{- 7} j^{6} (k^{6} k^{0})}$

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

$\frac{- 3 h}{- 9 h^{- 7} j^{6} k^{6 + 0}}$

Add $6$ and $0$ .

$\frac{- 3 h}{- 9 h^{- 7} j^{6} k^{6}}$

Step 3

Move $h^{- 7}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{- 3 h \cdot h^{7}}{- 9 j^{6} k^{6}}$

Step 4

Multiply $h$ by $h^{7}$ by adding the exponents.

Move $h^{7}$ .

$\frac{- 3 (h^{7} h)}{- 9 j^{6} k^{6}}$

Multiply $h^{7}$ by $h$ .

Raise $h$ to the power of $1$ .

$\frac{- 3 (h^{7} h^{1})}{- 9 j^{6} k^{6}}$

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

$\frac{- 3 h^{7 + 1}}{- 9 j^{6} k^{6}}$

Add $7$ and $1$ .

$\frac{- 3 h^{8}}{- 9 j^{6} k^{6}}$

Step 5

Cancel the common factor of $- 3$ and $- 9$ .

Factor $- 3$ out of $- 3 h^{8}$ .

$\frac{- 3 (h^{8})}{- 9 j^{6} k^{6}}$

Cancel the common factors.

Factor $- 3$ out of $- 9 j^{6} k^{6}$ .

$\frac{- 3 (h^{8})}{- 3 (3 j^{6} k^{6})}$

Cancel the common factor.

$\frac{- 3 h^{8}}{- 3 (3 j^{6} k^{6})}$

Rewrite the expression.

$\frac{h^{8}}{3 j^{6} k^{6}}$