Simplify (2/y)^4(4/y)^2

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

Step 1

Simplify the expression.

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

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

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

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

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

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

Step 2

Combine.

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

Step 3

Multiply $y^{4}$ by $y^{2}$ by adding the exponents.

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

$\frac{16 \cdot 4^{2}}{y^{4 + 2}}$

Add $4$ and $2$ .

$\frac{16 \cdot 4^{2}}{y^{6}}$

Step 4

Simplify the numerator.

Rewrite $16$ as $2^{4}$ .

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

Rewrite $4$ as $2^{2}$ .

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

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

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

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

Multiply $2$ by $2$ .

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

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

$\frac{2^{4 + 4}}{y^{6}}$

Add $4$ and $4$ .

$\frac{2^{8}}{y^{6}}$

Step 5

Raise $2$ to the power of $8$ .

$\frac{256}{y^{6}}$