Solve (4^frac{1{4}})^8+(3^-5)^frac{2{5}}

$$( 4 ^ { \frac { 1 } { 4 } } ) ^ { 8 } + ( 3 ^ { - 5 } ) ^ { \frac { 2 } { 5 } }$$

Evaluate

$$\frac{145}{9}\approx 16.111111111$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply \frac{1}{4} and 8 to get 2.

$$4^{2}+\left(3^{-5}\right)^{\frac{2}{5}}$$

To raise a power to another power, multiply the exponents. Multiply -5 and \frac{2}{5} to get -2.

$$4^{2}+3^{-2}$$

Calculate 4 to the power of 2 and get 16.

$$16+3^{-2}$$

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

$$16+\frac{1}{9}$$

Add 16 and \frac{1}{9} to get \frac{145}{9}.

$$\frac{145}{9}$$

Factor

$$\frac{5 \cdot 29}{3 ^ {2}} = 16\frac{1}{9} = 16.11111111111111$$