Algebra Examples

$\frac{{(y^{- 2})}^{- 6}}{- x^{4} y^{- 4} \cdot (- x) y^{4}}$

Step 1

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

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Step 1.1

Move $x$ .

$\frac{{(y^{- 2})}^{- 6}}{- (x \cdot x^{4}) y^{- 4} \cdot ((- 1) y^{4})}$

Step 1.2

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

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Step 1.2.1

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

$\frac{{(y^{- 2})}^{- 6}}{- (x^{1} x^{4}) y^{- 4} \cdot ((- 1) y^{4})}$

Step 1.2.2

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

$\frac{{(y^{- 2})}^{- 6}}{- x^{1 + 4} y^{- 4} \cdot ((- 1) y^{4})}$

Step 1.3

Add $1$ and $4$ .

$\frac{{(y^{- 2})}^{- 6}}{- x^{5} y^{- 4} \cdot ((- 1) y^{4})}$

Step 2

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

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Step 2.1

Move $y^{4}$ .

$\frac{{(y^{- 2})}^{- 6}}{- x^{5} (y^{4} y^{- 4}) \cdot - 1}$

Step 2.2

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

$\frac{{(y^{- 2})}^{- 6}}{- x^{5} y^{4 - 4} \cdot - 1}$

Step 2.3

Subtract $4$ from $4$ .

$\frac{{(y^{- 2})}^{- 6}}{- x^{5} y^{0} \cdot - 1}$

Step 3

Simplify $- x^{5} y^{0} \cdot - 1$ .

$\frac{{(y^{- 2})}^{- 6}}{- x^{5} \cdot - 1}$

Step 4

Move ${(y^{- 2})}^{- 6}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{- x^{5} \cdot - 1 {(y^{- 2})}^{6}}$

Step 5

Multiply $- 1$ by $- 1$ by adding the exponents.

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Step 5.1

Move $- 1$ .

$\frac{1}{- - 1 x^{5} {(y^{- 2})}^{6}}$

Step 5.2

Multiply $- 1$ by $- 1$ .

$\frac{1}{{(- 1)}^{2} x^{5} {(y^{- 2})}^{6}}$

Step 6

Simplify the denominator.

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Step 6.1

Raise $- 1$ to the power of $2$ .

$\frac{1}{1 x^{5} {(y^{- 2})}^{6}}$

Step 6.2

Multiply the exponents in ${(y^{- 2})}^{6}$ .

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Step 6.2.1

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

$\frac{1}{1 x^{5} y^{- 2 \cdot 6}}$

Step 6.2.2

Multiply $- 2$ by $6$ .

$\frac{1}{1 x^{5} y^{- 12}}$

Step 6.3

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

$\frac{1}{1 x^{5} \frac{1}{y^{12}}}$

Step 6.4

Combine exponents.

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Step 6.4.1

Multiply $x^{5}$ by $1$ .

$\frac{1}{x^{5} \frac{1}{y^{12}}}$

Step 6.4.2

Combine $x^{5}$ and $\frac{1}{y^{12}}$ .

$\frac{1}{\frac{x^{5}}{y^{12}}}$

Step 7

Multiply the numerator by the reciprocal of the denominator.

$1 \frac{y^{12}}{x^{5}}$

Step 8

Multiply $\frac{y^{12}}{x^{5}}$ by $1$ .

$\frac{y^{12}}{x^{5}}$