Simplify (7y^6)(2y^-4)^2

$(7 y^{6}) {(2 y^{- 4})}^{2}$

Step 1

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

$7 y^{6} {(2 \frac{1}{y^{4}})}^{2}$

Step 2

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

$7 y^{6} {(\frac{2}{y^{4}})}^{2}$

Step 3

Simplify the expression.

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

$7 y^{6} \frac{2^{2}}{{(y^{4})}^{2}}$

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

$7 y^{6} \frac{4}{{(y^{4})}^{2}}$

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

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

$7 y^{6} \frac{4}{y^{4 \cdot 2}}$

Multiply $4$ by $2$ .

$7 y^{6} \frac{4}{y^{8}}$

Step 4

Cancel the common factor of $y^{6}$ .

Factor $y^{6}$ out of $7 y^{6}$ .

$y^{6} \cdot 7 \frac{4}{y^{8}}$

Factor $y^{6}$ out of $y^{8}$ .

$y^{6} \cdot 7 \frac{4}{y^{6} y^{2}}$

Cancel the common factor.

$y^{6} \cdot 7 \frac{4}{y^{6} y^{2}}$

Rewrite the expression.

$7 \frac{4}{y^{2}}$

Step 5

Combine $7$ and $\frac{4}{y^{2}}$ .

$\frac{7 \cdot 4}{y^{2}}$

Step 6

Multiply $7$ by $4$ .

$\frac{28}{y^{2}}$