Solve (1/5)^-2(2/3)^3*(-3)^-2*3^5

$$( \frac { 1 } { 5 } ) ^ { - 2 } ( \frac { 2 } { 3 } ) ^ { 3 } \cdot ( - 3 ) ^ { - 2 } \cdot 3 ^ { 5 }$$

Evaluate

$$200$$

Solution Steps

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

$$25\times \left(\frac{2}{3}\right)^{3}\left(-3\right)^{-2}\times 3^{5}$$

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

$$25\times \frac{8}{27}\left(-3\right)^{-2}\times 3^{5}$$

Multiply 25 and \frac{8}{27} to get \frac{200}{27}.

$$\frac{200}{27}\left(-3\right)^{-2}\times 3^{5}$$

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

$$\frac{200}{27}\times \frac{1}{9}\times 3^{5}$$

Multiply \frac{200}{27} and \frac{1}{9} to get \frac{200}{243}.

$$\frac{200}{243}\times 3^{5}$$

Calculate 3 to the power of 5 and get 243.

$$\frac{200}{243}\times 243$$

Multiply \frac{200}{243} and 243 to get 200.

$$200$$

Factor

$$2^{3}\times 5^{2}$$