Algebra Examples

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

Step 1

Multiply $y^{2}$ by $y^{- 3}$ by adding the exponents.

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Step 1.1

Move $y^{- 3}$ .

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

Step 1.2

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

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

Step 1.3

Add $- 3$ and $2$ .

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

Step 2

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

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

Step 3

Simplify the numerator.

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Step 3.1

Apply the product rule to $x^{0} y^{2}$ .

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

Step 3.2

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

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Step 3.2.1

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

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

Step 3.2.2

Multiply $0$ by $3$ .

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

Step 3.3

Anything raised to $0$ is $1$ .

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

Step 3.4

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

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Step 3.4.1

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

$\frac{1 y^{2 \cdot 3} y}{2 x}$

Step 3.4.2

Multiply $2$ by $3$ .

$\frac{1 y^{6} y}{2 x}$

Step 3.5

Combine exponents.

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Step 3.5.1

Multiply $y^{6}$ by $1$ .

$\frac{y^{6} y}{2 x}$

Step 3.5.2

Multiply $y^{6}$ by $y$ by adding the exponents.

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Step 3.5.2.1

Multiply $y^{6}$ by $y$ .

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Step 3.5.2.1.1

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

$\frac{y^{6} y^{1}}{2 x}$

Step 3.5.2.1.2

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

$\frac{y^{6 + 1}}{2 x}$

Step 3.5.2.2

Add $6$ and $1$ .

$\frac{y^{7}}{2 x}$