Solve frac{(2^{2})^-1+(2^1)^-3}{2^-3}=

$$\frac { ( 2 ^ { 2 } ) ^ { - 1 } + ( 2 ^ { 1 } ) ^ { - 3 } } { 2 ^ { - 3 } } =$$

Evaluate

$$3$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and -1 to get -2.

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

To raise a power to another power, multiply the exponents. Multiply 1 and -3 to get -3.

$$\frac{2^{-2}+2^{-3}}{2^{-3}}$$

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

$$\frac{\frac{1}{4}+2^{-3}}{2^{-3}}$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

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

Add \frac{1}{4} and \frac{1}{8} to get \frac{3}{8}.

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

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$\frac{\frac{3}{8}}{\frac{1}{8}}$$

Divide \frac{3}{8} by \frac{1}{8} by multiplying \frac{3}{8} by the reciprocal of \frac{1}{8}.

$$\frac{3}{8}\times 8$$

Multiply \frac{3}{8} and 8 to get 3.

$$3$$

Factor

$$3$$