Simplify (3x^2)^2*(1/3x)^4

${(3 x^{2})}^{2} \cdot {(\frac{1}{3} x)}^{4}$

Simplify the expression.

Apply the product rule to $3 x^{2}$ .

$3^{2} {(x^{2})}^{2} \cdot {(\frac{1}{3} x)}^{4}$

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

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

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

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

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

Multiply $2$ by $2$ .

$9 x^{4} \cdot {(\frac{1}{3} x)}^{4}$

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

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

Simplify the expression.

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

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

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

$9 x^{4} \cdot \frac{x^{4}}{81}$

Cancel the common factor of $9$ .

Factor $9$ out of $9 x^{4}$ .

$9 (x^{4}) \cdot \frac{x^{4}}{81}$

Factor $9$ out of $81$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

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

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

Add $4$ and $4$ .

$\frac{x^{8}}{9}$