Algebra Examples

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

Step 1

Simplify the denominator.

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Step 1.1

Apply the product rule to $- 2 y^{- 5}$ .

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

Step 1.2

Raise $- 2$ to the power of $5$ .

$\frac{- 6 y^{4}}{- 32 {(y^{- 5})}^{5}}$

Step 1.3

Multiply the exponents in ${(y^{- 5})}^{5}$ .

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Step 1.3.1

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

$\frac{- 6 y^{4}}{- 32 y^{- 5 \cdot 5}}$

Step 1.3.2

Multiply $- 5$ by $5$ .

$\frac{- 6 y^{4}}{- 32 y^{- 25}}$

Step 1.4

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

$\frac{- 6 y^{4}}{- 32 \frac{1}{y^{25}}}$

Step 2

Combine $- 32$ and $\frac{1}{y^{25}}$ .

$\frac{- 6 y^{4}}{\frac{- 32}{y^{25}}}$

Step 3

Move the negative in front of the fraction.

$\frac{- 6 y^{4}}{- \frac{32}{y^{25}}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$- 6 y^{4} (- \frac{y^{25}}{32})$

Step 5

Cancel the common factor of $2$ .

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Step 5.1

Move the leading negative in $- \frac{y^{25}}{32}$ into the numerator.

$- 6 y^{4} \frac{- y^{25}}{32}$

Step 5.2

Factor $2$ out of $- 6 y^{4}$ .

$2 (- 3 y^{4}) \frac{- y^{25}}{32}$

Step 5.3

Factor $2$ out of $32$ .

$2 (- 3 y^{4}) \frac{- y^{25}}{2 (16)}$

Step 5.4

Cancel the common factor.

$2 (- 3 y^{4}) \frac{- y^{25}}{2 \cdot 16}$

Step 5.5

Rewrite the expression.

$- 3 y^{4} \frac{- y^{25}}{16}$

Step 6

Combine $- 3$ and $\frac{- y^{25}}{16}$ .

$y^{4} \frac{- 3 (- y^{25})}{16}$

Step 7

Multiply $- 1$ by $- 3$ .

$y^{4} \frac{3 y^{25}}{16}$

Step 8

Combine $y^{4}$ and $\frac{3 y^{25}}{16}$ .

$\frac{y^{4} (3 y^{25})}{16}$

Step 9

Multiply $y^{4}$ by $y^{25}$ by adding the exponents.

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Step 9.1

Move $y^{25}$ .

$\frac{y^{25} y^{4} \cdot 3}{16}$

Step 9.2

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

$\frac{y^{25 + 4} \cdot 3}{16}$

Step 9.3

Add $25$ and $4$ .

$\frac{y^{29} \cdot 3}{16}$

Step 10

Move $3$ to the left of $y^{29}$ .

$\frac{3 y^{29}}{16}$