Question

(xz^-2)^-3...........

Answer 1

$(xz^{-2})^{-3}= x^{-3} z^{6}$

Answer 2

To simplify the expression $(xz^{-2})^{-3}$, we need to apply the rules of exponents. When you raise a power to another power, you need to multiply the exponents. Let's break it down step by step:

Step 1: Apply the exponent outside the parentheses to both $x$ and $z^{-2}$.

$(xz^{-2})^{-3} = x^{-3}z^{(-2)(-3)}$

Step 2: Simplify the exponents.

$x^{-3}z^{(-2)(-3)} = x^{-3}z^{6}$

Step 3: Now, rewrite $x^{-3}$ as $\frac{1}{x^3}$.

$x^{-3}z^{6} = \frac{1}{x^3}z^{6}$

So, the simplified expression is $\frac{1}{x^3}z^{6}$.