Solve frac{2^frac{5{2}}*2^frac{1{2}}}{(16)^frac{3{2}}}

$$\frac { 2 ^ { \frac { 5 } { 2 } } \times 2 ^ { \frac { 1 } { 2 } } } { ( 16 ) ^ { \frac { 3 } { 2 } } }$$

Evaluate

$$\frac{1}{8}=0.125$$

Solution Steps

To multiply powers of the same base, add their exponents. Add \frac{5}{2} and \frac{1}{2} to get 3.

$$\frac{2^{3}}{16^{\frac{3}{2}}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8}{16^{\frac{3}{2}}}$$

Calculate 16 to the power of \frac{3}{2} and get 64.

$$\frac{8}{64}$$

Reduce the fraction \frac{8}{64} to lowest terms by extracting and canceling out 8.

$$\frac{1}{8}$$

Factor

$$\frac{1}{2 ^ {3}} = 0.125$$