Simplify (a^-3b^-3)^0

${(a^{- 3} b^{- 3})}^{0}$

Step 1

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

${(\frac{1}{a^{3}} b^{- 3})}^{0}$

Step 2

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

${(\frac{1}{a^{3}} \cdot \frac{1}{b^{3}})}^{0}$

Step 3

Combine.

${(\frac{1 \cdot 1}{a^{3} b^{3}})}^{0}$

Step 4

Multiply $1$ by $1$ .

${(\frac{1}{a^{3} b^{3}})}^{0}$

Step 5

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

Apply the product rule to $\frac{1}{a^{3} b^{3}}$ .

$\frac{1^{0}}{{(a^{3} b^{3})}^{0}}$

Apply the product rule to $a^{3} b^{3}$ .

$\frac{1^{0}}{{(a^{3})}^{0} {(b^{3})}^{0}}$

Step 6

Anything raised to $0$ is $1$ .

$\frac{1}{{(a^{3})}^{0} {(b^{3})}^{0}}$

Step 7

Simplify the denominator.

Multiply the exponents in ${(a^{3})}^{0}$ .

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

$\frac{1}{a^{3 \cdot 0} {(b^{3})}^{0}}$

Multiply $3$ by $0$ .

$\frac{1}{a^{0} {(b^{3})}^{0}}$

Anything raised to $0$ is $1$ .

$\frac{1}{1 {(b^{3})}^{0}}$

Multiply the exponents in ${(b^{3})}^{0}$ .

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

$\frac{1}{1 b^{3 \cdot 0}}$

Multiply $3$ by $0$ .

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

Anything raised to $0$ is $1$ .

$\frac{1}{1 \cdot 1}$

Multiply $1$ by $1$ .

$\frac{1}{1}$

Step 8

Divide $1$ by $1$ .

$1$