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

$$\frac { 2 ^ { - 2 } \cdot 2 ^ { 2 } + 2 : ( 3 ^ { 2 } ) ^ { 2 } + 18 ^ { 0 } } { 8 ^ { 2 / 3 } }$$

Evaluate

$$\frac{41}{81}\approx 0.50617284$$

Solution Steps

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

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

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

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

Calculate 3 to the power of 4 and get 81.

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

Add 1 and \frac{2}{81} to get \frac{83}{81}.

$$\frac{\frac{83}{81}+18^{0}}{8^{\frac{2}{3}}}$$

Calculate 18 to the power of 0 and get 1.

$$\frac{\frac{83}{81}+1}{8^{\frac{2}{3}}}$$

Add \frac{83}{81} and 1 to get \frac{164}{81}.

$$\frac{\frac{164}{81}}{8^{\frac{2}{3}}}$$

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

$$\frac{\frac{164}{81}}{4}$$

Express \frac{\frac{164}{81}}{4} as a single fraction.

$$\frac{164}{81\times 4}$$

Multiply 81 and 4 to get 324.

$$\frac{164}{324}$$

Reduce the fraction \frac{164}{324} to lowest terms by extracting and canceling out 4.

$$\frac{41}{81}$$

Factor

$$\frac{41}{3 ^ {4}} = 0.5061728395061729$$