Solve [(1/2)^2]^6*(2^3)^2

$$[ ( \frac { 1 } { 2 } ) ^ { 2 } ] ^ { 6 } \cdot ( 2 ^ { 3 } ) ^ { 2 }$$

Evaluate

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

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 6 to get 12.

$$\left(\frac{1}{2}\right)^{12}\times \left(2^{3}\right)^{2}$$

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

$$\left(\frac{1}{2}\right)^{12}\times 2^{6}$$

Calculate \frac{1}{2} to the power of 12 and get \frac{1}{4096}.

$$\frac{1}{4096}\times 2^{6}$$

Calculate 2 to the power of 6 and get 64.

$$\frac{1}{4096}\times 64$$

Multiply \frac{1}{4096} and 64 to get \frac{1}{64}.

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

Factor

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