Algebra Examples

${(p \frac{3}{2})}^{- 2}$

Step 1

Combine $p$ and $\frac{3}{2}$ .

${(\frac{p \cdot 3}{2})}^{- 2}$

Step 2

Move $3$ to the left of $p$ .

${(\frac{3 \cdot p}{2})}^{- 2}$

Step 3

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{2}{3 p})}^{2}$

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 $\frac{2}{3 p}$ .

$\frac{2^{2}}{{(3 p)}^{2}}$

Step 4.2

Apply the product rule to $3 p$ .

$\frac{2^{2}}{3^{2} p^{2}}$

Step 5

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

$\frac{4}{3^{2} p^{2}}$

Step 6

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

$\frac{4}{9 p^{2}}$