Simplify 3^-4(3x)^3

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

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.

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

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

Apply the product rule to $3 x$ .

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

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

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

Step 3

Cancel the common factor of $27$ .

Factor $27$ out of $81$ .

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

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

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