Simplify (6x^-3y^5)^0

${(6 x^{- 3} y^{5})}^{0}$

Step 1

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

${(6 \frac{1}{x^{3}} y^{5})}^{0}$

Step 2

Combine $6$ and $\frac{1}{x^{3}}$ .

${(\frac{6}{x^{3}} y^{5})}^{0}$

Step 3

Combine $\frac{6}{x^{3}}$ and $y^{5}$ .

${(\frac{6 y^{5}}{x^{3}})}^{0}$

Step 4

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

Apply the product rule to $\frac{6 y^{5}}{x^{3}}$ .

$\frac{{(6 y^{5})}^{0}}{{(x^{3})}^{0}}$

Apply the product rule to $6 y^{5}$ .

$\frac{6^{0} {(y^{5})}^{0}}{{(x^{3})}^{0}}$

Step 5

Simplify the numerator.

Anything raised to $0$ is $1$ .

$\frac{1 {(y^{5})}^{0}}{{(x^{3})}^{0}}$

Multiply the exponents in ${(y^{5})}^{0}$ .

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

$\frac{1 y^{5 \cdot 0}}{{(x^{3})}^{0}}$

Multiply $5$ by $0$ .

$\frac{1 y^{0}}{{(x^{3})}^{0}}$

Anything raised to $0$ is $1$ .

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

Multiply $1$ by $1$ .

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

Step 6

Simplify the denominator.

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

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

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

Multiply $3$ by $0$ .

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

Anything raised to $0$ is $1$ .

$\frac{1}{1}$

Step 7

Divide $1$ by $1$ .

$1$