Solve {left(1/2right)}^6*2^6/2^3*{left(1/2right)}^-2

$${ \left( \frac{ 1 }{ 2 } \right) }^{ 6 } \times \frac{ { 2 }^{ 6 } }{ { 2 }^{ 3 } } \times { \left( \frac{ 1 }{ 2 } \right) }^{ -2 }$$

Evaluate

$$\frac{1}{2}=0.5$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 3 from 6 to get 3.

$$\left(\frac{1}{2}\right)^{6}\times 2^{3}\times \left(\frac{1}{2}\right)^{-2}$$

To multiply powers of the same base, add their exponents. Add 6 and -2 to get 4.

$$\left(\frac{1}{2}\right)^{4}\times 2^{3}$$

Calculate \frac{1}{2} to the power of 4 and get \frac{1}{16}.

$$\frac{1}{16}\times 2^{3}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{1}{16}\times 8$$

Multiply \frac{1}{16} and 8 to get \frac{1}{2}.

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$