Algebra Examples

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

Step 1

Move ${(4 x^{- 3} y^{2})}^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 2

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

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

Step 3

Combine $3$ and $\frac{1}{x^{5}}$ .

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

Step 4

Combine $\frac{3}{x^{5}}$ and $y^{2}$ .

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

Step 5

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

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Step 5.1

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

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

Step 5.2

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

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

Step 6

Simplify the numerator.

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Step 6.1

Anything raised to $0$ is $1$ .

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

Step 6.2

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

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Step 6.2.1

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

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

Step 6.2.2

Multiply $2$ by $0$ .

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

Step 6.3

Anything raised to $0$ is $1$ .

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

Step 6.4

Multiply $1$ by $1$ .

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

Step 7

Simplify the denominator.

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Step 7.1

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

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Step 7.1.1

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

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

Step 7.1.2

Multiply $5$ by $0$ .

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

Step 7.2

Anything raised to $0$ is $1$ .

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

Step 8

Simplify the expression.

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Step 8.1

Divide $1$ by $1$ .

$1 {(4 x^{- 3} y^{2})}^{2}$

Step 8.2

Multiply ${(4 x^{- 3} y^{2})}^{2}$ by $1$ .

${(4 x^{- 3} y^{2})}^{2}$

Step 9

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

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

Step 10

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

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

Step 11

Combine $\frac{4}{x^{3}}$ and $y^{2}$ .

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

Step 12

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

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Step 12.1

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

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

Step 12.2

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

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

Step 13

Simplify the numerator.

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Step 13.1

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

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

Step 13.2

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

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Step 13.2.1

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

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

Step 13.2.2

Multiply $2$ by $2$ .

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

Step 14

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

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Step 14.1

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

$\frac{16 y^{4}}{x^{3 \cdot 2}}$

Step 14.2

Multiply $3$ by $2$ .

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