Basic Math Examples

${(6 a^{- 3} p^{3})}^{- 2}$

Step 1

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

${(6 \frac{1}{a^{3}} p^{3})}^{- 2}$

Step 2

Combine $6$ and $\frac{1}{a^{3}}$ .

${(\frac{6}{a^{3}} p^{3})}^{- 2}$

Step 3

Combine $\frac{6}{a^{3}}$ and $p^{3}$ .

${(\frac{6 p^{3}}{a^{3}})}^{- 2}$

Step 4

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

${(\frac{a^{3}}{6 p^{3}})}^{2}$

Step 5

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

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Step 5.1

Apply the product rule to $\frac{a^{3}}{6 p^{3}}$ .

$\frac{{(a^{3})}^{2}}{{(6 p^{3})}^{2}}$

Step 5.2

Apply the product rule to $6 p^{3}$ .

$\frac{{(a^{3})}^{2}}{6^{2} {(p^{3})}^{2}}$

Step 6

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

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Step 6.1

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

$\frac{a^{3 \cdot 2}}{6^{2} {(p^{3})}^{2}}$

Step 6.2

Multiply $3$ by $2$ .

$\frac{a^{6}}{6^{2} {(p^{3})}^{2}}$

Step 7

Simplify the denominator.

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Step 7.1

Raise $6$ to the power of $2$ .

$\frac{a^{6}}{36 {(p^{3})}^{2}}$

Step 7.2

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

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Step 7.2.1

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

$\frac{a^{6}}{36 p^{3 \cdot 2}}$

Step 7.2.2

Multiply $3$ by $2$ .

$\frac{a^{6}}{36 p^{6}}$