Solve frac{((3^{10})^frac{1{2}})^frac{1{3}}}{(3^2)^frac{1{3}}}

$$\frac { ( ( 3 ^ { 10 } ) ^ { \frac { 1 } { 2 } } ) ^ { \frac { 1 } { 3 } } } { ( 3 ^ { 2 } ) ^ { \frac { 1 } { 3 } } }$$

Evaluate

$$3$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 10 and \frac{1}{2} to get 5.

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

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

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

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

$$\frac{3^{\frac{5}{3}}}{3^{\frac{2}{3}}}$$

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

$$3^{1}$$

Calculate 3 to the power of 1 and get 3.

$$3$$

Factor

$$3$$