Algebra Examples

$3^{- 3} {(6 p^{- 5})}^{2}$

Step 1

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

$\frac{1}{3^{3}} {(6 p^{- 5})}^{2}$

Step 2

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

$\frac{1}{27} {(6 p^{- 5})}^{2}$

Step 3

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

$\frac{1}{27} {(6 \frac{1}{p^{5}})}^{2}$

Step 4

Combine $6$ and $\frac{1}{p^{5}}$ .

$\frac{1}{27} {(\frac{6}{p^{5}})}^{2}$

Step 5

Apply the product rule to $\frac{6}{p^{5}}$ .

$\frac{1}{27} \cdot \frac{6^{2}}{{(p^{5})}^{2}}$

Step 6

Combine.

$\frac{1 \cdot 6^{2}}{27 {(p^{5})}^{2}}$

Step 7

Simplify the expression.

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Step 7.1

Multiply $6^{2}$ by $1$ .

$\frac{6^{2}}{27 {(p^{5})}^{2}}$

Step 7.2

Multiply the exponents in ${(p^{5})}^{2}$ .

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Step 7.2.1

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

$\frac{6^{2}}{27 p^{5 \cdot 2}}$

Step 7.2.2

Multiply $5$ by $2$ .

$\frac{6^{2}}{27 p^{10}}$

Step 7.3

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

$\frac{36}{27 p^{10}}$

Step 8

Cancel the common factor of $36$ and $27$ .

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Step 8.1

Factor $9$ out of $36$ .

$\frac{9 (4)}{27 p^{10}}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $9$ out of $27 p^{10}$ .

$\frac{9 (4)}{9 (3 p^{10})}$

Step 8.2.2

Cancel the common factor.

$\frac{9 \cdot 4}{9 (3 p^{10})}$

Step 8.2.3

Rewrite the expression.

$\frac{4}{3 p^{10}}$