Algebra Examples

$9 n^{2} {(\frac{1}{3} n)}^{4}$

Step 1

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

$9 n^{2} {(\frac{n}{3})}^{4}$

Step 2

Simplify the expression.

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Step 2.1

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

$9 n^{2} \frac{n^{4}}{3^{4}}$

Step 2.2

Raise $3$ to the power of $4$ .

$9 n^{2} \frac{n^{4}}{81}$

Step 3

Cancel the common factor of $9$ .

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Step 3.1

Factor $9$ out of $9 n^{2}$ .

$9 (n^{2}) \frac{n^{4}}{81}$

Step 3.2

Factor $9$ out of $81$ .

$9 (n^{2}) \frac{n^{4}}{9 (9)}$

Step 3.3

Cancel the common factor.

$9 n^{2} \frac{n^{4}}{9 \cdot 9}$

Step 3.4

Rewrite the expression.

$n^{2} \frac{n^{4}}{9}$

Step 4

Combine $n^{2}$ and $\frac{n^{4}}{9}$ .

$\frac{n^{2} n^{4}}{9}$

Step 5

Multiply $n^{2}$ by $n^{4}$ by adding the exponents.

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Step 5.1

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

$\frac{n^{2 + 4}}{9}$

Step 5.2

Add $2$ and $4$ .

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