Solve 321/5+{left(1/27right)}^frac{-2{3}}-{left(1/25right)}^-frac{3{2}}+81^3

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

Evaluate

$$\frac{2656786}{5}=531357.2$$

Solution Steps

Multiply 32 and 5 to get 160.

$$\frac{160+1}{5}+\left(\frac{1}{27}\right)^{\frac{-2}{3}}-\left(\frac{1}{25}\right)^{-\frac{3}{2}}+81^{3}$$

Add 160 and 1 to get 161.

$$\frac{161}{5}+\left(\frac{1}{27}\right)^{\frac{-2}{3}}-\left(\frac{1}{25}\right)^{-\frac{3}{2}}+81^{3}$$

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

$$\frac{161}{5}+\left(\frac{1}{27}\right)^{-\frac{2}{3}}-\left(\frac{1}{25}\right)^{-\frac{3}{2}}+81^{3}$$

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

$$\frac{161}{5}+9-\left(\frac{1}{25}\right)^{-\frac{3}{2}}+81^{3}$$

Add \frac{161}{5} and 9 to get \frac{206}{5}.

$$\frac{206}{5}-\left(\frac{1}{25}\right)^{-\frac{3}{2}}+81^{3}$$

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

$$\frac{206}{5}-125+81^{3}$$

Subtract 125 from \frac{206}{5} to get -\frac{419}{5}.

$$-\frac{419}{5}+81^{3}$$

Calculate 81 to the power of 3 and get 531441.

$$-\frac{419}{5}+531441$$

Add -\frac{419}{5} and 531441 to get \frac{2656786}{5}.

$$\frac{2656786}{5}$$

Factor

$$\frac{2 \cdot 11 \cdot 120763}{5} = 531357\frac{1}{5} = 531357.2$$