Simplify ((4ab^2)/(5ab))^2

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

Step 1

Cancel the common factor of $a$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

Cancel the common factor of $b^{2}$ and $b$ .

Factor $b$ out of $4 b^{2}$ .

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

Cancel the common factors.

Factor $b$ out of $5 b$ .

${(\frac{b (4 b)}{b \cdot 5})}^{2}$

Cancel the common factor.

${(\frac{b (4 b)}{b \cdot 5})}^{2}$

Rewrite the expression.

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

Step 3

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

Apply the product rule to $\frac{4 b}{5}$ .

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

Apply the product rule to $4 b$ .

$\frac{4^{2} b^{2}}{5^{2}}$

Step 4

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

$\frac{16 b^{2}}{5^{2}}$

Step 5

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

$\frac{16 b^{2}}{25}$