Solve frac{(54^frac{1{2}})^frac{5{3}}}{54^frac{1{2}}}

$$\frac { ( 54 ^ { \frac { 1 } { 2 } } ) ^ { \frac { 5 } { 3 } } } { 54 ^ { \frac { 1 } { 2 } } }$$

Evaluate

$$3\sqrt[3]{2}\approx 3.77976315$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply \frac{1}{2} and \frac{5}{3} to get \frac{5}{6}.

$$\frac{54^{\frac{5}{6}}}{54^{\frac{1}{2}}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract \frac{1}{2} from \frac{5}{6} to get \frac{1}{3}.

$$54^{\frac{1}{3}}$$