Solve 1/3*(25/4)^frac{1{2}}*(4/9)^0+(125/64)^frac{1{3}}

$$\frac { 1 } { 3 } \times ( \frac { 25 } { 4 } ) ^ { \frac { 1 } { 2 } } \times ( \frac { 4 } { 9 } ) ^ { 0 } + ( \frac { 125 } { 64 } ) ^ { \frac { 1 } { 3 } }$$

Evaluate

$$\frac{25}{12}\approx 2.083333333$$

Solution Steps

Calculate \frac{25}{4} to the power of \frac{1}{2} and get \frac{5}{2}.

$$\frac{1}{3}\times \frac{5}{2}\times \left(\frac{4}{9}\right)^{0}+\left(\frac{125}{64}\right)^{\frac{1}{3}}$$

Multiply \frac{1}{3} and \frac{5}{2} to get \frac{5}{6}.

$$\frac{5}{6}\times \left(\frac{4}{9}\right)^{0}+\left(\frac{125}{64}\right)^{\frac{1}{3}}$$

Calculate \frac{4}{9} to the power of 0 and get 1.

$$\frac{5}{6}\times 1+\left(\frac{125}{64}\right)^{\frac{1}{3}}$$

Multiply \frac{5}{6} and 1 to get \frac{5}{6}.

$$\frac{5}{6}+\left(\frac{125}{64}\right)^{\frac{1}{3}}$$

Calculate \frac{125}{64} to the power of \frac{1}{3} and get \frac{5}{4}.

$$\frac{5}{6}+\frac{5}{4}$$

Add \frac{5}{6} and \frac{5}{4} to get \frac{25}{12}.

$$\frac{25}{12}$$

Factor

$$\frac{5 ^ {2}}{2 ^ {2} \cdot 3} = 2\frac{1}{12} = 2.0833333333333335$$