Solve (8/27)^-frac{1{3}}*(25/4)^frac{1{2}}*(4/9)^0+(125/64)^frac{1{3}}

$$( \frac { 8 } { 27 } ) ^ { - \frac { 1 } { 3 } } \times ( \frac { 25 } { 4 } ) ^ { \frac { 1 } { 2 } } \times ( \frac { 4 } { 9 } ) ^ { 0 } + ( \frac { 125 } { 64 } ) ^ { \frac { 1 } { 3 } }$$

Evaluate

$$5$$

Solution Steps

Calculate \frac{8}{27} to the power of -\frac{1}{3} and get \frac{3}{2}.

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

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

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

Multiply \frac{3}{2} and \frac{5}{2} to get \frac{15}{4}.

$$\frac{15}{4}\times \left(\frac{4}{9}\right)^{0}+\left(\frac{125}{64}\right)^{\frac{1}{3}}$$

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

$$\frac{15}{4}\times 1+\left(\frac{125}{64}\right)^{\frac{1}{3}}$$

Multiply \frac{15}{4} and 1 to get \frac{15}{4}.

$$\frac{15}{4}+\left(\frac{125}{64}\right)^{\frac{1}{3}}$$

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

$$\frac{15}{4}+\frac{5}{4}$$

Add \frac{15}{4} and \frac{5}{4} to get 5.

$$5$$

Factor

$$5$$