Simplify ((x^-2)/(x^5))^0

${(\frac{x^{- 2}}{x^{5}})}^{0}$

Step 1

Move $x^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{1}{x^{5} x^{2}})}^{0}$

Step 2

Multiply $x^{5}$ by $x^{2}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(\frac{1}{x^{5 + 2}})}^{0}$

Add $5$ and $2$ .

${(\frac{1}{x^{7}})}^{0}$

Step 3

Simplify the expression.

Apply the product rule to $\frac{1}{x^{7}}$ .

$\frac{1^{0}}{{(x^{7})}^{0}}$

Anything raised to $0$ is $1$ .

$\frac{1}{{(x^{7})}^{0}}$

Step 4

Simplify the denominator.

Multiply the exponents in ${(x^{7})}^{0}$ .

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

$\frac{1}{x^{7 \cdot 0}}$

Multiply $7$ by $0$ .

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

Anything raised to $0$ is $1$ .

$\frac{1}{1}$

Step 5

Divide $1$ by $1$ .

$1$