Simplify -(2x^-2yz)^0

$- {(2 x^{- 2} y z)}^{0}$

Step 1

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

$- {(2 \frac{1}{x^{2}} y z)}^{0}$

Step 2

Combine $2$ and $\frac{1}{x^{2}}$ .

$- {(\frac{2}{x^{2}} y z)}^{0}$

Step 3

Combine $\frac{2}{x^{2}}$ and $y$ .

$- {(\frac{2 y}{x^{2}} z)}^{0}$

Step 4

Combine $\frac{2 y}{x^{2}}$ and $z$ .

$- {(\frac{2 y z}{x^{2}})}^{0}$

Step 5

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $\frac{2 y z}{x^{2}}$ .

$- \frac{{(2 y z)}^{0}}{{(x^{2})}^{0}}$

Apply the product rule to $2 y z$ .

$- \frac{{(2 y)}^{0} z^{0}}{{(x^{2})}^{0}}$

Apply the product rule to $2 y$ .

$- \frac{2^{0} y^{0} z^{0}}{{(x^{2})}^{0}}$

Step 6

Simplify the numerator.

Anything raised to $0$ is $1$ .

$- \frac{1 y^{0} z^{0}}{{(x^{2})}^{0}}$

Anything raised to $0$ is $1$ .

$- \frac{1 \cdot 1 z^{0}}{{(x^{2})}^{0}}$

Anything raised to $0$ is $1$ .

$- \frac{1 \cdot 1 \cdot 1}{{(x^{2})}^{0}}$

Combine exponents.

Multiply $1$ by $1$ .

$- \frac{1 \cdot 1}{{(x^{2})}^{0}}$

Multiply $1$ by $1$ .

$- \frac{1}{{(x^{2})}^{0}}$

Step 7

Simplify the denominator.

Multiply the exponents in ${(x^{2})}^{0}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- \frac{1}{x^{2 \cdot 0}}$

Multiply $2$ by $0$ .

$- \frac{1}{x^{0}}$

Anything raised to $0$ is $1$ .

$- \frac{1}{1}$

Step 8

Reduce the expression by cancelling the common factors.

Cancel the common factor of $1$ .

Cancel the common factor.

$- \frac{1}{1}$

Rewrite the expression.

$- 1 \cdot 1$

Multiply $- 1$ by $1$ .

$- 1$

Simplify -(2x^-2yz)^0

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