Simplify (2ab^-1)^2

${(2 a b^{- 1})}^{2}$

Step 1

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

${(2 a \frac{1}{b})}^{2}$

Step 2

Multiply $2 a \frac{1}{b}$ .

Combine $2$ and $\frac{1}{b}$ .

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

Combine $a$ and $\frac{2}{b}$ .

${(\frac{a \cdot 2}{b})}^{2}$

Step 3

Move $2$ to the left of $a$ .

${(\frac{2 \cdot a}{b})}^{2}$

Step 4

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

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

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

Apply the product rule to $2 a$ .

$\frac{2^{2} a^{2}}{b^{2}}$

Step 5

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

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