Solve (frac{13^frac{3{2}}}{169^frac{1{2}}})^frac{3{2}}

$$( \frac { 13 ^ { \frac { 3 } { 2 } } } { 169 ^ { \frac { 1 } { 2 } } } ) ^ { \frac { 3 } { 2 } }$$

Evaluate

$$13^{\frac{3}{4}}\approx 6.846325042$$

Solution Steps

Calculate 169 to the power of \frac{1}{2} and get 13.

$$\left(\frac{13^{\frac{3}{2}}}{13}\right)^{\frac{3}{2}}$$

To raise \frac{13^{\frac{3}{2}}}{13} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(13^{\frac{3}{2}}\right)^{\frac{3}{2}}}{13^{\frac{3}{2}}}$$

To raise a power to another power, multiply the exponents. Multiply \frac{3}{2} and \frac{3}{2} to get \frac{9}{4}.

$$\frac{13^{\frac{9}{4}}}{13^{\frac{3}{2}}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract \frac{3}{2} from \frac{9}{4} to get \frac{3}{4}.

$$13^{\frac{3}{4}}$$