Simplify ((8g^-3h)^-1)/(2g^2h^-1)

$\frac{{(8 g^{- 3} h)}^{- 1}}{2 g^{2} h^{- 1}}$

Move ${(8 g^{- 3} h)}^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{2 g^{2} h^{- 1} (8 g^{- 3} h)}$

Simplify the denominator.

Multiply $g^{2}$ by $g^{- 3}$ by adding the exponents.

Move $g^{- 3}$ .

$\frac{1}{2 (g^{- 3} g^{2}) h^{- 1} (8 h)}$

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

$\frac{1}{2 g^{- 3 + 2} h^{- 1} (8 h)}$

Add $- 3$ and $2$ .

$\frac{1}{2 g^{- 1} h^{- 1} (8 h)}$

Multiply $h^{- 1}$ by $h$ by adding the exponents.

Move $h$ .

$\frac{1}{2 g^{- 1} (h \cdot h^{- 1}) \cdot 8}$

Multiply $h$ by $h^{- 1}$ .

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

$\frac{1}{2 g^{- 1} (h^{1} h^{- 1}) \cdot 8}$

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

$\frac{1}{2 g^{- 1} h^{1 - 1} \cdot 8}$

Subtract $1$ from $1$ .

$\frac{1}{2 g^{- 1} h^{0} \cdot 8}$

Simplify $2 g^{- 1} h^{0} \cdot 8$ .

$\frac{1}{2 g^{- 1} \cdot 8}$

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

$\frac{g}{2 \cdot 8}$

Multiply $2$ by $8$ .

$\frac{g}{16}$