Simplify (3x)^(2/3)(3x)^(7/3)

${(3 x)}^{\frac{2}{3}} {(3 x)}^{\frac{7}{3}}$

Multiply ${(3 x)}^{\frac{2}{3}}$ by ${(3 x)}^{\frac{7}{3}}$ by adding the exponents.

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

${(3 x)}^{\frac{2}{3} + \frac{7}{3}}$

Combine the numerators over the common denominator.

${(3 x)}^{\frac{2 + 7}{3}}$

Add $2$ and $7$ .

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

Divide $9$ by $3$ .

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

Apply the product rule to $3 x$ .

$3^{3} x^{3}$

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

$27 x^{3}$