Simplify ((3x)^(1/3)*(3x)^(7/3))/((3x)^(2/3))

$\frac{{(3 x)}^{\frac{1}{3}} \cdot {(3 x)}^{\frac{7}{3}}}{{(3 x)}^{\frac{2}{3}}}$

Step 1

Multiply ${(3 x)}^{\frac{1}{3}}$ by ${(3 x)}^{\frac{7}{3}}$ by adding the exponents.

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

$\frac{{(3 x)}^{\frac{1}{3} + \frac{7}{3}}}{{(3 x)}^{\frac{2}{3}}}$

Combine the numerators over the common denominator.

$\frac{{(3 x)}^{\frac{1 + 7}{3}}}{{(3 x)}^{\frac{2}{3}}}$

Add $1$ and $7$ .

$\frac{{(3 x)}^{\frac{8}{3}}}{{(3 x)}^{\frac{2}{3}}}$

Step 2

Move ${(3 x)}^{\frac{2}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

${(3 x)}^{\frac{8}{3}} {(3 x)}^{- \frac{2}{3}}$

Step 3

Multiply ${(3 x)}^{\frac{8}{3}}$ by ${(3 x)}^{- \frac{2}{3}}$ by adding the exponents.

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

${(3 x)}^{\frac{8}{3} - \frac{2}{3}}$

Combine the numerators over the common denominator.

${(3 x)}^{\frac{8 - 2}{3}}$

Subtract $2$ from $8$ .

${(3 x)}^{\frac{6}{3}}$

Divide $6$ by $3$ .

${(3 x)}^{2}$

Step 4

Apply the product rule to $3 x$ .

$3^{2} x^{2}$

Step 5

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

$9 x^{2}$