Algebra Examples

${(- 3^{- 2} y)}^{2}$

Step 1

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

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

Step 2

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

${(- \frac{1}{9} y)}^{2}$

Step 3

Combine $y$ and $\frac{1}{9}$ .

${(- \frac{y}{9})}^{2}$

Step 4

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

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Step 4.1

Apply the product rule to $- \frac{y}{9}$ .

${(- 1)}^{2} {(\frac{y}{9})}^{2}$

Step 4.2

Apply the product rule to $\frac{y}{9}$ .

${(- 1)}^{2} \frac{y^{2}}{9^{2}}$

Step 5

Raise $- 1$ to the power of $2$ .

$1 \frac{y^{2}}{9^{2}}$

Step 6

Multiply $\frac{y^{2}}{9^{2}}$ by $1$ .

$\frac{y^{2}}{9^{2}}$

Step 7

Raise $9$ to the power of $2$ .

$\frac{y^{2}}{81}$