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

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

Evaluate

$$\frac{929}{27}\approx 34.407407407$$

Solution Steps

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

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

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

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

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

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

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

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

Calculate 3 to the power of 3 and get 27.

$$\frac{200}{27}+27$$

Add \frac{200}{27} and 27 to get \frac{929}{27}.

$$\frac{929}{27}$$

Factor

$$\frac{929}{3 ^ {3}} = 34\frac{11}{27} = 34.407407407407405$$