Algebra Examples

$\frac{- 12 y^{- 8}}{{(- 3 y^{- 1})}^{4}}$

Step 1

Move $y^{- 8}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{- 12}{{(- 3 y^{- 1})}^{4} y^{8}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $- 3 y^{- 1}$ .

$\frac{- 12}{{(- 3)}^{4} {(y^{- 1})}^{4} y^{8}}$

Step 2.2

Raise $- 3$ to the power of $4$ .

$\frac{- 12}{81 {(y^{- 1})}^{4} y^{8}}$

Step 2.3

Multiply the exponents in ${(y^{- 1})}^{4}$ .

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Step 2.3.1

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

$\frac{- 12}{81 y^{- 1 \cdot 4} y^{8}}$

Step 2.3.2

Multiply $- 1$ by $4$ .

$\frac{- 12}{81 y^{- 4} y^{8}}$

Step 2.4

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

$\frac{- 12}{81 \frac{1}{y^{4}} y^{8}}$

Step 2.5

Combine exponents.

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Step 2.5.1

Combine $81$ and $\frac{1}{y^{4}}$ .

$\frac{- 12}{\frac{81}{y^{4}} y^{8}}$

Step 2.5.2

Combine $\frac{81}{y^{4}}$ and $y^{8}$ .

$\frac{- 12}{\frac{81 y^{8}}{y^{4}}}$

Step 2.6

Reduce the expression by cancelling the common factors.

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Step 2.6.1

Reduce the expression $\frac{81 y^{8}}{y^{4}}$ by cancelling the common factors.

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Step 2.6.1.1

Factor $y^{4}$ out of $81 y^{8}$ .

$\frac{- 12}{\frac{y^{4} (81 y^{4})}{y^{4}}}$

Step 2.6.1.2

Multiply by $1$ .

$\frac{- 12}{\frac{y^{4} (81 y^{4})}{y^{4} \cdot 1}}$

Step 2.6.1.3

Cancel the common factor.

$\frac{- 12}{\frac{y^{4} (81 y^{4})}{y^{4} \cdot 1}}$

Step 2.6.1.4

Rewrite the expression.

$\frac{- 12}{\frac{81 y^{4}}{1}}$

Step 2.6.2

Divide $81 y^{4}$ by $1$ .

$\frac{- 12}{81 y^{4}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $- 12$ and $81$ .

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Step 3.1.1

Factor $3$ out of $- 12$ .

$\frac{3 (- 4)}{81 y^{4}}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $3$ out of $81 y^{4}$ .

$\frac{3 (- 4)}{3 (27 y^{4})}$

Step 3.1.2.2

Cancel the common factor.

$\frac{3 \cdot - 4}{3 (27 y^{4})}$

Step 3.1.2.3

Rewrite the expression.

$\frac{- 4}{27 y^{4}}$

Step 3.2

Move the negative in front of the fraction.

$- \frac{4}{27 y^{4}}$