Solve left(2^-5right)^22^-6/2^-18{left(1/2right)}^3

$$\frac{ { \left( { 2 }^{ -5 } \right) }^{ 2 } { 2 }^{ -6 } }{ { 2 }^{ -18 } } { \left( \frac{ 1 }{ 2 } \right) }^{ 3 }$$

Evaluate

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

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -5 and 2 to get -10.

$$\frac{2^{-10}\times 2^{-6}}{2^{-18}}\times \left(\frac{1}{2}\right)^{3}$$

To multiply powers of the same base, add their exponents. Add -10 and -6 to get -16.

$$\frac{2^{-16}}{2^{-18}}\times \left(\frac{1}{2}\right)^{3}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -18 from -16 to get 2.

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

Calculate 2 to the power of 2 and get 4.

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

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

$$4\times \frac{1}{8}$$

Multiply 4 and \frac{1}{8} to get \frac{1}{2}.

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

Factor

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