Question

1. simplify.

$- x^{3}y^{-2}(- x^{0})^{-1}$

Explanation:

Step1: Simplify $x^0$

Any non-zero number to the 0 power is 1, so $x^0 = 1$.
The expression becomes: $-x^3y^{-2}(-1)^{-1}$

Step2: Simplify $(-1)^{-1}$

A negative exponent means reciprocal, so $(-1)^{-1} = \frac{1}{-1} = -1$.
The expression becomes: $-x^3y^{-2}(-1)$

Step3: Multiply the constant terms

Multiply $-1$ and $-1$: $(-1) \times (-1) = 1$.
The expression becomes: $1 \times x^3y^{-2} = x^3y^{-2}$

Step4: Rewrite positive exponent for $y$

A negative exponent moves the term to the denominator: $y^{-2} = \frac{1}{y^2}$.
The expression becomes: $\frac{x^3}{y^2}$

Answer:

$\frac{x^3}{y^2}$