Algebra Examples

$3^{- 4} {(3 x)}^{3}$

Step 1

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

$\frac{1}{3^{4}} {(3 x)}^{3}$

Step 2

Simplify the expression.

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Step 2.1

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

$\frac{1}{81} {(3 x)}^{3}$

Step 2.2

Apply the product rule to $3 x$ .

$\frac{1}{81} (3^{3} x^{3})$

Step 2.3

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

$\frac{1}{81} (27 x^{3})$

Step 3

Cancel the common factor of $27$ .

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Step 3.1

Factor $27$ out of $81$ .

$\frac{1}{27 (3)} (27 x^{3})$

Step 3.2

Factor $27$ out of $27 x^{3}$ .

$\frac{1}{27 (3)} (27 (x^{3}))$

Step 3.3

Cancel the common factor.

$\frac{1}{27 \cdot 3} (27 x^{3})$

Step 3.4

Rewrite the expression.

$\frac{1}{3} x^{3}$

Step 4

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

$\frac{x^{3}}{3}$