Solve (1/2)^-2+125^frac{2{3}}+343^frac{1{3}}-(1/27)^-frac{1{3}}

$$( \frac { 1 } { 2 } ) ^ { - 2 } + 125 ^ { \frac { 2 } { 3 } } + 343 ^ { \frac { 1 } { 3 } } - ( \frac { 1 } { 27 } ) ^ { - \frac { 1 } { 3 } }$$

Evaluate

$$33$$

Solution Steps

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

$$4+125^{\frac{2}{3}}+343^{\frac{1}{3}}-\left(\frac{1}{27}\right)^{-\frac{1}{3}}$$

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

$$4+25+343^{\frac{1}{3}}-\left(\frac{1}{27}\right)^{-\frac{1}{3}}$$

Add 4 and 25 to get 29.

$$29+343^{\frac{1}{3}}-\left(\frac{1}{27}\right)^{-\frac{1}{3}}$$

Calculate 343 to the power of \frac{1}{3} and get 7.

$$29+7-\left(\frac{1}{27}\right)^{-\frac{1}{3}}$$

Add 29 and 7 to get 36.

$$36-\left(\frac{1}{27}\right)^{-\frac{1}{3}}$$

Calculate \frac{1}{27} to the power of -\frac{1}{3} and get 3.

$$36-3$$

Subtract 3 from 36 to get 33.

$$33$$

Factor

$$3\times 11$$