Write the Fraction in Simplest Form ((-4y)^3)/(4y^-8)

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

Step 1

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

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

Step 2

Simplify the numerator.

Apply the product rule to $- 4 y$ .

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

Multiply $y^{3}$ by $y^{8}$ by adding the exponents.

Move $y^{8}$ .

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

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

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

Add $8$ and $3$ .

$\frac{{(- 4)}^{3} y^{11}}{4}$

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

$\frac{- 64 y^{11}}{4}$

Step 3

Cancel the common factor of $- 64$ and $4$ .

Factor $4$ out of $- 64 y^{11}$ .

$\frac{4 (- 16 y^{11})}{4}$

Cancel the common factors.

Factor $4$ out of $4$ .

$\frac{4 (- 16 y^{11})}{4 (1)}$

Cancel the common factor.

$\frac{4 (- 16 y^{11})}{4 \cdot 1}$

Rewrite the expression.

$\frac{- 16 y^{11}}{1}$

Divide $- 16 y^{11}$ by $1$ .

$- 16 y^{11}$