Pre-Algebra Examples

${(\frac{p^{- 2}}{3 p^{- 5}})}^{- 2}$

Step 1

Move $p^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{p^{- 2} p^{5}}{3})}^{- 2}$

Step 2

Multiply $p^{- 2}$ by $p^{5}$ by adding the exponents.

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Step 2.1

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

${(\frac{p^{- 2 + 5}}{3})}^{- 2}$

Step 2.2

Add $- 2$ and $5$ .

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

Step 3

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

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

Step 4

Apply the product rule to $\frac{3}{p^{3}}$ .

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

Step 5

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

$\frac{9}{{(p^{3})}^{2}}$

Step 6

Multiply the exponents in ${(p^{3})}^{2}$ .

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Step 6.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{9}{p^{3 \cdot 2}}$

Step 6.2

Multiply $3$ by $2$ .

$\frac{9}{p^{6}}$