Solve {32}^frac{4{5}}+{left(1/27right)}^frac{-2{3}}-{left(1/25right)}^-frac{3{2}}+{81}^frac{1{4}}

$${ 32 }^{ \frac{ 4 }{ 5 } } + { \left( \frac{ 1 }{ 27 } \right) }^{ \frac{ -2 }{ 3 } } - { \left( \frac{ 1 }{ 25 } \right) }^{ - \frac{ 3 }{ 2 } } + { 81 }^{ \frac{ 1 }{ 4 } }$$

Evaluate

$$-97$$

Solution Steps

Calculate 32 to the power of \frac{4}{5} and get 16.

$$16+\left(\frac{1}{27}\right)^{\frac{-2}{3}}-\left(\frac{1}{25}\right)^{-\frac{3}{2}}+81^{\frac{1}{4}}$$

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$16+\left(\frac{1}{27}\right)^{-\frac{2}{3}}-\left(\frac{1}{25}\right)^{-\frac{3}{2}}+81^{\frac{1}{4}}$$

Calculate \frac{1}{27} to the power of -\frac{2}{3} and get 9.

$$16+9-\left(\frac{1}{25}\right)^{-\frac{3}{2}}+81^{\frac{1}{4}}$$

Add 16 and 9 to get 25.

$$25-\left(\frac{1}{25}\right)^{-\frac{3}{2}}+81^{\frac{1}{4}}$$

Calculate \frac{1}{25} to the power of -\frac{3}{2} and get 125.

$$25-125+81^{\frac{1}{4}}$$

Subtract 125 from 25 to get -100.

$$-100+81^{\frac{1}{4}}$$

Calculate 81 to the power of \frac{1}{4} and get 3.

$$-100+3$$

Add -100 and 3 to get -97.

$$-97$$

Factor

$$-97$$