Simplify (5^-2x^-9)/(4^-2y^5z^-2)

$\frac{5^{- 2} x^{- 9}}{4^{- 2} y^{5} z^{- 2}}$

Move $5^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{x^{- 9}}{4^{- 2} y^{5} z^{- 2} \cdot 5^{2}}$

Move $x^{- 9}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{4^{- 2} y^{5} z^{- 2} \cdot 5^{2} x^{9}}$

Move $4^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{4^{2}}{y^{5} z^{- 2} \cdot 5^{2} x^{9}}$

Move $z^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{4^{2} z^{2}}{y^{5} \cdot 5^{2} x^{9}}$

Raise $4$ to the power of $2$ .

$\frac{16 z^{2}}{y^{5} \cdot 5^{2} x^{9}}$

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

$\frac{16 z^{2}}{y^{5} \cdot 25 x^{9}}$

Move $25$ to the left of $y^{5}$ .

$\frac{16 z^{2}}{25 y^{5} x^{9}}$