Algebra Examples

$\frac{4 x^{0} y^{- 2}}{4 x y^{- 4}}$

Step 1

Move $x^{0}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{4 y^{- 2}}{4 x y^{- 4} x^{0}}$

Step 2

Simplify the denominator.

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Step 2.1

Multiply $x$ by $x^{0}$ by adding the exponents.

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Step 2.1.1

Move $x^{0}$ .

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

Step 2.1.2

Multiply $x^{0}$ by $x$ .

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Step 2.1.2.1

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

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

Step 2.1.2.2

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

$\frac{4 y^{- 2}}{4 x^{0 + 1} y^{- 4}}$

Step 2.1.3

Add $0$ and $1$ .

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

Step 2.2

Simplify $4 x^{1} y^{- 4}$ .

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

Step 3

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

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

Step 4

Multiply $y^{- 2}$ by $y^{4}$ by adding the exponents.

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Step 4.1

Move $y^{4}$ .

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

Step 4.2

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

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

Step 4.3

Subtract $2$ from $4$ .

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

Step 5

Cancel the common factor of $4$ .

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Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

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