Solve 3^frac{2{3}}*3^frac{3{2}}div3^frac{1{6}}

$$3 ^ { \frac { 2 } { 3 } } \times 3 ^ { \frac { 3 } { 2 } } \div 3 ^ { \frac { 1 } { 6 } }$$

Evaluate

$$9$$

Solution Steps

To multiply powers of the same base, add their exponents. Add \frac{2}{3} and \frac{3}{2} to get \frac{13}{6}.

$$\frac{3^{\frac{13}{6}}}{3^{\frac{1}{6}}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract \frac{1}{6} from \frac{13}{6} to get 2.

$$3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9$$

Factor

$$3^{2}$$