Solve 3^-2*(frac{1/5)^-3*sqrt[3]{27}}{3-1/3-2*(-1/2+1)}=

$$\frac { 3 ^ { - 2 } \cdot ( \frac { 1 } { 5 } ) ^ { - 3 } \cdot \sqrt[ 3 ] { 27 } } { 3 - \frac { 1 } { 3 } - 2 \cdot ( - \frac { 1 } { 2 } + 1 ) } =$$

Evaluate

$$25$$

Solution Steps

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

$$\frac{\frac{1}{9}\times \left(\frac{1}{5}\right)^{-3}\sqrt[3]{27}}{3-\frac{1}{3}-2\left(-\frac{1}{2}+1\right)}$$

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

$$\frac{\frac{1}{9}\times 125\sqrt[3]{27}}{3-\frac{1}{3}-2\left(-\frac{1}{2}+1\right)}$$

Multiply \frac{1}{9} and 125 to get \frac{125}{9}.

$$\frac{\frac{125}{9}\sqrt[3]{27}}{3-\frac{1}{3}-2\left(-\frac{1}{2}+1\right)}$$

Calculate \sqrt[3]{27} and get 3.

$$\frac{\frac{125}{9}\times 3}{3-\frac{1}{3}-2\left(-\frac{1}{2}+1\right)}$$

Multiply \frac{125}{9} and 3 to get \frac{125}{3}.

$$\frac{\frac{125}{3}}{3-\frac{1}{3}-2\left(-\frac{1}{2}+1\right)}$$

Subtract \frac{1}{3} from 3 to get \frac{8}{3}.

$$\frac{\frac{125}{3}}{\frac{8}{3}-2\left(-\frac{1}{2}+1\right)}$$

Add -\frac{1}{2} and 1 to get \frac{1}{2}.

$$\frac{\frac{125}{3}}{\frac{8}{3}-2\times \frac{1}{2}}$$

Multiply 2 and \frac{1}{2} to get 1.

$$\frac{\frac{125}{3}}{\frac{8}{3}-1}$$

Subtract 1 from \frac{8}{3} to get \frac{5}{3}.

$$\frac{\frac{125}{3}}{\frac{5}{3}}$$

Divide \frac{125}{3} by \frac{5}{3} by multiplying \frac{125}{3} by the reciprocal of \frac{5}{3}.

$$\frac{125}{3}\times \frac{3}{5}$$

Multiply \frac{125}{3} and \frac{3}{5} to get 25.

$$25$$

Factor

$$5^{2}$$