Solve frac{(25)^frac{1{2}}}{(64)^frac{1{3}}}+(256/625)^-1/4+(64/125)^-2/3

$$\frac { ( 25 ) ^ { \frac { 1 } { 2 } } } { ( 64 ) ^ { \frac { 1 } { 3 } } } + ( \frac { 256 } { 625 } ) ^ { - 1 / 4 } + ( \frac { 64 } { 125 } ) ^ { - 2 / 3 }$$

Evaluate

$$\frac{65}{16}=4.0625$$

Solution Steps

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

$$\frac{5}{64^{\frac{1}{3}}}+\left(\frac{256}{625}\right)^{-\frac{1}{4}}+\left(\frac{64}{125}\right)^{-\frac{2}{3}}$$

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

$$\frac{5}{4}+\left(\frac{256}{625}\right)^{-\frac{1}{4}}+\left(\frac{64}{125}\right)^{-\frac{2}{3}}$$

Calculate \frac{256}{625} to the power of -\frac{1}{4} and get \frac{5}{4}.

$$\frac{5}{4}+\frac{5}{4}+\left(\frac{64}{125}\right)^{-\frac{2}{3}}$$

Add \frac{5}{4} and \frac{5}{4} to get \frac{5}{2}.

$$\frac{5}{2}+\left(\frac{64}{125}\right)^{-\frac{2}{3}}$$

Calculate \frac{64}{125} to the power of -\frac{2}{3} and get \frac{25}{16}.

$$\frac{5}{2}+\frac{25}{16}$$

Add \frac{5}{2} and \frac{25}{16} to get \frac{65}{16}.

$$\frac{65}{16}$$

Factor

$$\frac{5 \cdot 13}{2 ^ {4}} = 4\frac{1}{16} = 4.0625$$