Simplify ((2y^2)^4)/(-10y^-1)

$\frac{{(2 y^{2})}^{4}}{- 10 y^{- 1}}$

Step 1

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

$\frac{{(2 y^{2})}^{4} y}{- 10}$

Step 2

Simplify the numerator.

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

$\frac{2^{4} {(y^{2})}^{4} y}{- 10}$

Raise $2$ to the power of $4$ .

$\frac{16 {(y^{2})}^{4} y}{- 10}$

Multiply the exponents in ${(y^{2})}^{4}$ .

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

$\frac{16 y^{2 \cdot 4} y}{- 10}$

Multiply $2$ by $4$ .

$\frac{16 y^{8} y}{- 10}$

Combine exponents.

Raise $y$ to the power of $1$ .

$\frac{16 (y^{1} y^{8})}{- 10}$

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

$\frac{16 y^{1 + 8}}{- 10}$

Add $1$ and $8$ .

$\frac{16 y^{9}}{- 10}$

Step 3

Reduce the expression by cancelling the common factors.

Cancel the common factor of $16$ and $- 10$ .

Factor $2$ out of $16 y^{9}$ .

$\frac{2 (8 y^{9})}{- 10}$

Cancel the common factors.

Factor $2$ out of $- 10$ .

$\frac{2 (8 y^{9})}{2 (- 5)}$

Cancel the common factor.

$\frac{2 (8 y^{9})}{2 \cdot - 5}$

Rewrite the expression.

$\frac{8 y^{9}}{- 5}$

Move the negative in front of the fraction.

$- \frac{8 y^{9}}{5}$