Algebra Examples

$\frac{3 {(y^{- 4})}^{4}}{12 y^{- 6}}$

Step 1

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

$\frac{3 {(y^{- 4})}^{4} y^{6}}{12}$

Step 2

Cancel the common factor of $3$ and $12$ .

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Step 2.1

Factor $3$ out of $3 {(y^{- 4})}^{4} y^{6}$ .

$\frac{3 ({(y^{- 4})}^{4} y^{6})}{12}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $3$ out of $12$ .

$\frac{3 ({(y^{- 4})}^{4} y^{6})}{3 \cdot 4}$

Step 2.2.2

Cancel the common factor.

$\frac{3 ({(y^{- 4})}^{4} y^{6})}{3 \cdot 4}$

Step 2.2.3

Rewrite the expression.

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

Step 3

Simplify the numerator.

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Step 3.1

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

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Step 3.1.1

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

$\frac{y^{- 4 \cdot 4} y^{6}}{4}$

Step 3.1.2

Multiply $- 4$ by $4$ .

$\frac{y^{- 16} y^{6}}{4}$

Step 3.2

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

$\frac{\frac{1}{y^{16}} y^{6}}{4}$

Step 4

Combine $\frac{1}{y^{16}}$ and $y^{6}$ .

$\frac{\frac{y^{6}}{y^{16}}}{4}$

Step 5

Reduce the expression $\frac{y^{6}}{y^{16}}$ by cancelling the common factors.

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Step 5.1

Multiply by $1$ .

$\frac{\frac{y^{6} \cdot 1}{y^{16}}}{4}$

Step 5.2

Factor $y^{6}$ out of $y^{16}$ .

$\frac{\frac{y^{6} \cdot 1}{y^{6} y^{10}}}{4}$

Step 5.3

Cancel the common factor.

$\frac{\frac{y^{6} \cdot 1}{y^{6} y^{10}}}{4}$

Step 5.4

Rewrite the expression.

$\frac{\frac{1}{y^{10}}}{4}$

Step 6

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{y^{10}} \cdot \frac{1}{4}$

Step 7

Combine.

$\frac{1 \cdot 1}{y^{10} \cdot 4}$

Step 8

Multiply $1$ by $1$ .

$\frac{1}{y^{10} \cdot 4}$

Step 9

Move $4$ to the left of $y^{10}$ .

$\frac{1}{4 y^{10}}$