Simplify 4^-2x^3y^-5z^0

$4^{- 2} x^{3} y^{- 5} z^{0}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{4^{2}} x^{3} y^{- 5} z^{0}$

Step 2

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

$\frac{1}{16} x^{3} y^{- 5} z^{0}$

Step 3

Combine $\frac{1}{16}$ and $x^{3}$ .

$\frac{x^{3}}{16} y^{- 5} z^{0}$

Step 4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{x^{3}}{16} \cdot \frac{1}{y^{5}} z^{0}$

Step 5

Combine.

$\frac{x^{3} \cdot 1}{16 y^{5}} z^{0}$

Step 6

Simplify the expression.

Multiply $x^{3}$ by $1$ .

$\frac{x^{3}}{16 y^{5}} z^{0}$

Anything raised to $0$ is $1$ .

$\frac{x^{3}}{16 y^{5}} \cdot 1$

Multiply $\frac{x^{3}}{16 y^{5}}$ by $1$ .

$\frac{x^{3}}{16 y^{5}}$