Simplify ((-1/2)y^4)^3*(-16y^2)

${((- \frac{1}{2}) y^{4})}^{3} \cdot (- 16 y^{2})$

Rewrite using the commutative property of multiplication.

$- 16 {(- \frac{1}{2} y^{4})}^{3} y^{2}$

Combine $y^{4}$ and $\frac{1}{2}$ .

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

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $- \frac{y^{4}}{2}$ .

$- 16 ({(- 1)}^{3} {(\frac{y^{4}}{2})}^{3}) y^{2}$

Apply the product rule to $\frac{y^{4}}{2}$ .

$- 16 ({(- 1)}^{3} \frac{{(y^{4})}^{3}}{2^{3}}) y^{2}$

Simplify the expression.

Raise $- 1$ to the power of $3$ .

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

Multiply the exponents in ${(y^{4})}^{3}$ .

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

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

Multiply $4$ by $3$ .

$- 16 (- \frac{y^{12}}{2^{3}}) y^{2}$

Raise $2$ to the power of $3$ .

$- 16 (- \frac{y^{12}}{8}) y^{2}$

Cancel the common factor of $8$ .

Move the leading negative in $- \frac{y^{12}}{8}$ into the numerator.

$- 16 \frac{- y^{12}}{8} y^{2}$

Factor $8$ out of $- 16$ .

$8 (- 2) \frac{- y^{12}}{8} y^{2}$

Cancel the common factor.

$8 \cdot - 2 \frac{- y^{12}}{8} y^{2}$

Rewrite the expression.

$- 2 (- y^{12}) y^{2}$

Multiply $- 1$ by $- 2$ .

$2 y^{12} y^{2}$

Multiply $y^{12}$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

$2 (y^{2} y^{12})$

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

$2 y^{2 + 12}$

Add $2$ and $12$ .

$2 y^{14}$