Simplify (3x^4)(x/3)^3

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

Step 1

Simplify the expression.

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

$3 x^{4} \frac{x^{3}}{3^{3}}$

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

$3 x^{4} \frac{x^{3}}{27}$

Step 2

Cancel the common factor of $3$ .

Factor $3$ out of $3 x^{4}$ .

$3 (x^{4}) \frac{x^{3}}{27}$

Factor $3$ out of $27$ .

$3 (x^{4}) \frac{x^{3}}{3 (9)}$

Cancel the common factor.

$3 x^{4} \frac{x^{3}}{3 \cdot 9}$

Rewrite the expression.

$x^{4} \frac{x^{3}}{9}$

Step 3

Combine $x^{4}$ and $\frac{x^{3}}{9}$ .

$\frac{x^{4} x^{3}}{9}$

Step 4

Multiply $x^{4}$ by $x^{3}$ by adding the exponents.

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

$\frac{x^{4 + 3}}{9}$

Add $4$ and $3$ .

$\frac{x^{7}}{9}$