Simplify the expression $x^3 y^0 z^{-7}$

What you are simplifying here

This expression has two special exponent cases: a zero exponent ($y^0$) and a negative exponent ($z^{-7}$). The goal is to rewrite it using only positive exponents.

Use the zero-exponent rule

For any nonzero base $a$, $$a^0 = 1.$$ So, $$y^0 = 1.$$ That means $$x^3 y^0 z^{-7} = x^3 \cdot 1 \cdot z^{-7} = x^3 z^{-7}.$$

Rewrite the negative exponent

A negative exponent moves the factor to the denominator: $$a^{-n} = \frac{1}{a^n}.$$ So, $$z^{-7} = \frac{1}{z^7}.$$ Therefore, $$x^3 z^{-7} = x^3 \cdot \frac{1}{z^7} = \frac{x^3}{z^7}.$$

Final simplified form

$$\frac{x^3}{z^7}$$