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

To multiply powers of the same base, add their exponents. Add -2 and 5 to get 3.

$$\left(\frac{1}{5}\right)^{-2}\times \left(\frac{2}{3}\right)^{3}\times 3^{3}$$

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

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

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

$$25\times \frac{8}{27}\times 3^{3}$$

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

$$\frac{200}{27}\times 3^{3}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{200}{27}\times 27$$

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

$$200$$

Factor

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