Simplify ((k^-2y^3)/(y^-1))^0

${(\frac{k^{- 2} y^{3}}{y^{- 1}})}^{0}$

Step 1

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

${(\frac{y^{3}}{y^{- 1} k^{2}})}^{0}$

Step 2

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

${(\frac{y^{3} y}{k^{2}})}^{0}$

Step 3

Multiply $y^{3}$ by $y$ by adding the exponents.

Multiply $y^{3}$ by $y$ .

Raise $y$ to the power of $1$ .

${(\frac{y^{3} y^{1}}{k^{2}})}^{0}$

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

${(\frac{y^{3 + 1}}{k^{2}})}^{0}$

Add $3$ and $1$ .

${(\frac{y^{4}}{k^{2}})}^{0}$

Step 4

Apply the product rule to $\frac{y^{4}}{k^{2}}$ .

$\frac{{(y^{4})}^{0}}{{(k^{2})}^{0}}$

Step 5

Simplify the numerator.

Multiply the exponents in ${(y^{4})}^{0}$ .

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

$\frac{y^{4 \cdot 0}}{{(k^{2})}^{0}}$

Multiply $4$ by $0$ .

$\frac{y^{0}}{{(k^{2})}^{0}}$

Anything raised to $0$ is $1$ .

$\frac{1}{{(k^{2})}^{0}}$

Step 6

Simplify the denominator.

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

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

$\frac{1}{k^{2 \cdot 0}}$

Multiply $2$ by $0$ .

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

Anything raised to $0$ is $1$ .

$\frac{1}{1}$

Step 7

Divide $1$ by $1$ .

$1$