Algebra Examples

$\frac{x y}{7 x^{- 4} y^{- 2}}$

Step 1

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

$\frac{x y x^{4}}{7 y^{- 2}}$

Step 2

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

$\frac{x y x^{4} y^{2}}{7}$

Step 3

Simplify the numerator.

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Step 3.1

Multiply $x$ by $x^{4}$ by adding the exponents.

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Step 3.1.1

Move $x^{4}$ .

$\frac{x^{4} x y \cdot y^{2}}{7}$

Step 3.1.2

Multiply $x^{4}$ by $x$ .

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Step 3.1.2.1

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

$\frac{x^{4} x^{1} y \cdot y^{2}}{7}$

Step 3.1.2.2

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

$\frac{x^{4 + 1} y \cdot y^{2}}{7}$

Step 3.1.3

Add $4$ and $1$ .

$\frac{x^{5} y \cdot y^{2}}{7}$

Step 3.2

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

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Step 3.2.1

Move $y^{2}$ .

$\frac{x^{5} (y^{2} y)}{7}$

Step 3.2.2

Multiply $y^{2}$ by $y$ .

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Step 3.2.2.1

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

$\frac{x^{5} (y^{2} y^{1})}{7}$

Step 3.2.2.2

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

$\frac{x^{5} y^{2 + 1}}{7}$

Step 3.2.3

Add $2$ and $1$ .

$\frac{x^{5} y^{3}}{7}$