Simplify -(6y^4)/((-2y^-5)^5)

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

Step 1

Simplify the denominator.

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

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

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

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

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

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

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

Multiply $- 5$ by $5$ .

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

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 fractions.

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

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

Move the negative in front of the fraction.

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

Step 3

Multiply the numerator by the reciprocal of the denominator.

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

Step 4

Cancel the common factor of $2$ .

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

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

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

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

Factor $2$ out of $32$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 5

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

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

Step 6

Multiply $- 1$ by $3$ .

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

Step 7

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

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

Step 8

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

Move $y^{25}$ .

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

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

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

Add $25$ and $4$ .

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

Step 9

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

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

Step 10

Move the negative in front of the fraction.

$- - \frac{(3) \cdot y^{29}}{16}$

Step 11

Multiply $- - \frac{3 y^{29}}{16}$ .

Multiply $- 1$ by $- 1$ .

$1 \frac{3 y^{29}}{16}$

Multiply $\frac{3 y^{29}}{16}$ by $1$ .

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

Simplify -(6y^4)/((-2y^-5)^5)

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