Simplify ((x^-3y^5)/(4^-3))^0

${(\frac{x^{- 3} y^{5}}{4^{- 3}})}^{0}$

Step 1

Move $x^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{y^{5}}{4^{- 3} x^{3}})}^{0}$

Step 2

Move $4^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{y^{5} \cdot 4^{3}}{x^{3}})}^{0}$

Step 3

Raise $4$ to the power of $3$ .

${(\frac{y^{5} \cdot 64}{x^{3}})}^{0}$

Step 4

Move $64$ to the left of $y^{5}$ .

${(\frac{64 \cdot y^{5}}{x^{3}})}^{0}$

Step 5

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

Apply the product rule to $\frac{64 y^{5}}{x^{3}}$ .

$\frac{{(64 y^{5})}^{0}}{{(x^{3})}^{0}}$

Apply the product rule to $64 y^{5}$ .

$\frac{64^{0} {(y^{5})}^{0}}{{(x^{3})}^{0}}$

Step 6

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 7

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 8

Divide $1$ by $1$ .

$1$