Simplify (4/5a^2)^2

${(\frac{4}{5} a^{2})}^{2}$

Step 1

Combine $\frac{4}{5}$ and $a^{2}$ .

${(\frac{4 a^{2}}{5})}^{2}$

Step 2

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

Apply the product rule to $\frac{4 a^{2}}{5}$ .

$\frac{{(4 a^{2})}^{2}}{5^{2}}$

Apply the product rule to $4 a^{2}$ .

$\frac{4^{2} {(a^{2})}^{2}}{5^{2}}$

Step 3

Simplify the numerator.

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

$\frac{16 {(a^{2})}^{2}}{5^{2}}$

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

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

$\frac{16 a^{2 \cdot 2}}{5^{2}}$

Multiply $2$ by $2$ .

$\frac{16 a^{4}}{5^{2}}$

Step 4

Raise $5$ to the power of $2$ .

$\frac{16 a^{4}}{25}$