Algebra Examples

$\frac{{(4 x^{- 3} y^{2})}^{2}}{{(2 x^{3} y^{5})}^{0}}$

Step 1

Simplify the numerator.

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Step 1.1

Apply the product rule to $4 x^{- 3} y^{2}$ .

$\frac{{(4 x^{- 3})}^{2} {(y^{2})}^{2}}{{(2 x^{3} y^{5})}^{0}}$

Step 1.2

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

$\frac{{(4 \frac{1}{x^{3}})}^{2} {(y^{2})}^{2}}{{(2 x^{3} y^{5})}^{0}}$

Step 1.3

Combine $4$ and $\frac{1}{x^{3}}$ .

$\frac{{(\frac{4}{x^{3}})}^{2} {(y^{2})}^{2}}{{(2 x^{3} y^{5})}^{0}}$

Step 1.4

Apply the product rule to $\frac{4}{x^{3}}$ .

$\frac{\frac{4^{2}}{{(x^{3})}^{2}} {(y^{2})}^{2}}{{(2 x^{3} y^{5})}^{0}}$

Step 1.5

Raise $4$ to the power of $2$ .

$\frac{\frac{16}{{(x^{3})}^{2}} {(y^{2})}^{2}}{{(2 x^{3} y^{5})}^{0}}$

Step 1.6

Multiply the exponents in ${(x^{3})}^{2}$ .

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Step 1.6.1

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

$\frac{\frac{16}{x^{3 \cdot 2}} {(y^{2})}^{2}}{{(2 x^{3} y^{5})}^{0}}$

Step 1.6.2

Multiply $3$ by $2$ .

$\frac{\frac{16}{x^{6}} {(y^{2})}^{2}}{{(2 x^{3} y^{5})}^{0}}$

Step 1.7

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

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Step 1.7.1

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

$\frac{\frac{16}{x^{6}} y^{2 \cdot 2}}{{(2 x^{3} y^{5})}^{0}}$

Step 1.7.2

Multiply $2$ by $2$ .

$\frac{\frac{16}{x^{6}} y^{4}}{{(2 x^{3} y^{5})}^{0}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $2 x^{3} y^{5}$ .

$\frac{\frac{16}{x^{6}} y^{4}}{{(2 x^{3})}^{0} {(y^{5})}^{0}}$

Step 2.2

Apply the product rule to $2 x^{3}$ .

$\frac{\frac{16}{x^{6}} y^{4}}{2^{0} {(x^{3})}^{0} {(y^{5})}^{0}}$

Step 2.3

Anything raised to $0$ is $1$ .

$\frac{\frac{16}{x^{6}} y^{4}}{1 {(x^{3})}^{0} {(y^{5})}^{0}}$

Step 2.4

Multiply ${(x^{3})}^{0}$ by $1$ .

$\frac{\frac{16}{x^{6}} y^{4}}{{(x^{3})}^{0} {(y^{5})}^{0}}$

Step 2.5

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

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Step 2.5.1

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

$\frac{\frac{16}{x^{6}} y^{4}}{x^{3 \cdot 0} {(y^{5})}^{0}}$

Step 2.5.2

Multiply $3$ by $0$ .

$\frac{\frac{16}{x^{6}} y^{4}}{x^{0} {(y^{5})}^{0}}$

Step 2.6

Anything raised to $0$ is $1$ .

$\frac{\frac{16}{x^{6}} y^{4}}{1 {(y^{5})}^{0}}$

Step 2.7

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

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Step 2.7.1

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

$\frac{\frac{16}{x^{6}} y^{4}}{1 y^{5 \cdot 0}}$

Step 2.7.2

Multiply $5$ by $0$ .

$\frac{\frac{16}{x^{6}} y^{4}}{1 y^{0}}$

Step 2.8

Anything raised to $0$ is $1$ .

$\frac{\frac{16}{x^{6}} y^{4}}{1 \cdot 1}$

Step 2.9

Multiply $1$ by $1$ .

$\frac{\frac{16}{x^{6}} y^{4}}{1}$

Step 3

Combine fractions.

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Step 3.1

Combine $\frac{16}{x^{6}}$ and $y^{4}$ .

$\frac{\frac{16 y^{4}}{x^{6}}}{1}$

Step 3.2

Divide $\frac{16 y^{4}}{x^{6}}$ by $1$ .

$\frac{16 y^{4}}{x^{6}}$