Basic Math Examples

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

Step 1

Move $p^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 2

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

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Step 2.1

Move $p^{2}$ .

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

Step 2.2

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

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

Step 2.3

Add $2$ and $5$ .

${(3 p^{7})}^{- 2}$

Step 3

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

$\frac{1}{{(3 p^{7})}^{2}}$

Step 4

Simplify the denominator.

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Step 4.1

Apply the product rule to $3 p^{7}$ .

$\frac{1}{3^{2} {(p^{7})}^{2}}$

Step 4.2

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

$\frac{1}{9 {(p^{7})}^{2}}$

Step 4.3

Multiply the exponents in ${(p^{7})}^{2}$ .

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Step 4.3.1

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

$\frac{1}{9 p^{7 \cdot 2}}$

Step 4.3.2

Multiply $7$ by $2$ .

$\frac{1}{9 p^{14}}$