Solve frac{(2^{-2})^3}{(2^-1*2^-4)^0}

$$\frac { ( 2 ^ { - 2 } ) ^ { 3 } } { ( 2 ^ { - 1 } \cdot 2 ^ { - 4 } ) ^ { 0 } }$$

Evaluate

$$\frac{1}{64}=0.015625$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -2 and 3 to get -6.

$$\frac{2^{-6}}{\left(2^{-1}\times 2^{-4}\right)^{0}}$$

To multiply powers of the same base, add their exponents. Add -1 and -4 to get -5.

$$\frac{2^{-6}}{\left(2^{-5}\right)^{0}}$$

To raise a power to another power, multiply the exponents. Multiply -5 and 0 to get 0.

$$\frac{2^{-6}}{2^{0}}$$

Rewrite 2^{0} as 2^{-6}\times 2^{6}. Cancel out 2^{-6} in both numerator and denominator.

$$\frac{1}{2^{6}}$$

Calculate 2 to the power of 6 and get 64.

$$\frac{1}{64}$$

Factor

$$\frac{1}{2 ^ {6}} = 0.015625$$