Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

Combine $3$ and $\frac{1}{n^{3}}$ .

$\frac{6}{n^{5}} {(\frac{3}{n^{3}})}^{2}$

Step 5

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

$\frac{6}{n^{5}} \cdot \frac{3^{2}}{{(n^{3})}^{2}}$

Step 6

Combine.

$\frac{6 \cdot 3^{2}}{n^{5} {(n^{3})}^{2}}$

Step 7

Simplify the expression.

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Step 7.1

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

$\frac{6 \cdot 9}{n^{5} {(n^{3})}^{2}}$

Step 7.2

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

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Step 7.2.1

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

$\frac{6 \cdot 9}{n^{5} n^{3 \cdot 2}}$

Step 7.2.2

Multiply $3$ by $2$ .

$\frac{6 \cdot 9}{n^{5} n^{6}}$

Step 7.3

Multiply $6$ by $9$ .

$\frac{54}{n^{5} n^{6}}$

Step 8

Multiply $n^{5}$ by $n^{6}$ by adding the exponents.

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Step 8.1

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

$\frac{54}{n^{5 + 6}}$

Step 8.2

Add $5$ and $6$ .

$\frac{54}{n^{11}}$