Simplify (2^2y^-6)/(8^-1z^0x^-7)

$\frac{2^{2} y^{- 6}}{8^{- 1} z^{0} x^{- 7}}$

Simplify the expression.

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

$\frac{2^{2}}{8^{- 1} z^{0} x^{- 7} y^{6}}$

Move $8^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{2^{2} \cdot 8}{x^{- 7} y^{6}}$

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

$\frac{2^{2} \cdot 8 x^{7}}{y^{6}}$

Simplify the numerator.

Rewrite $8$ as $2^{3}$ .

$\frac{2^{2} \cdot 2^{3} x^{7}}{y^{6}}$

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

$\frac{2^{2 + 3} x^{7}}{y^{6}}$

Add $2$ and $3$ .

$\frac{2^{5} x^{7}}{y^{6}}$

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

$\frac{32 x^{7}}{y^{6}}$