Solve frac{2^{-2}*2^{2}+2*(3^2)^2+18^0}{8^frac{2{3}}}

$$\frac { 2 ^ { - 2 } \times 2 ^ { 2 } + 2 \times ( 3 ^ { 2 } ) ^ { 2 } + 18 ^ { 0 } } { 8 ^ { \frac { 2 } { 3 } } }$$

Evaluate

$$41$$

Solution Steps

Multiply 2^{-2} and 2^{2} to get 1.

$$\frac{1+2\times \left(3^{2}\right)^{2}+18^{0}}{8^{\frac{2}{3}}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{1+2\times 3^{4}+18^{0}}{8^{\frac{2}{3}}}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{1+2\times 81+18^{0}}{8^{\frac{2}{3}}}$$

Multiply 2 and 81 to get 162.

$$\frac{1+162+18^{0}}{8^{\frac{2}{3}}}$$

Add 1 and 162 to get 163.

$$\frac{163+18^{0}}{8^{\frac{2}{3}}}$$

Calculate 18 to the power of 0 and get 1.

$$\frac{163+1}{8^{\frac{2}{3}}}$$

Add 163 and 1 to get 164.

$$\frac{164}{8^{\frac{2}{3}}}$$

Calculate 8 to the power of \frac{2}{3} and get 4.

$$\frac{164}{4}$$

Divide 164 by 4 to get 41.

$$41$$

Factor

$$41$$