Solve (2^{-3}div2^-2)+(2^2)^2-2^-2

$$( 2 ^ { - 3 } \div 2 ^ { - 2 } ) + ( 2 ^ { 2 } ) ^ { 2 } - 2 ^ { - 2 }$$

Evaluate

$$\frac{65}{4}=16.25$$

Solution Steps

Rewrite 2^{-2} as 2\times 2^{-3}. Cancel out 2^{-3} in both numerator and denominator.

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

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

$$\frac{1}{2}+2^{4}-2^{-2}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{1}{2}+16-2^{-2}$$

Add \frac{1}{2} and 16 to get \frac{33}{2}.

$$\frac{33}{2}-2^{-2}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$\frac{33}{2}-\frac{1}{4}$$

Subtract \frac{1}{4} from \frac{33}{2} to get \frac{65}{4}.

$$\frac{65}{4}$$

Factor

$$\frac{5 \cdot 13}{2 ^ {2}} = 16\frac{1}{4} = 16.25$$