Simplify ((3^0)/(3^-1))^2

${(\frac{3^{0}}{3^{- 1}})}^{2}$

Step 1

Move $3^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(3^{0} \cdot 3)}^{2}$

Step 2

Multiply $3^{0}$ by $3$ by adding the exponents.

Multiply $3^{0}$ by $3$ .

Raise $3$ to the power of $1$ .

${(3^{0} \cdot 3^{1})}^{2}$

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

${(3^{0 + 1})}^{2}$

Add $0$ and $1$ .

${(3^{1})}^{2}$

Step 3

Simplify $3^{1}$ .

$3^{2}$

Step 4

Raise $3$ to the power of $2$ .

$9$