Solve left(2^3div2^5right)^4*2^-5

$${ \left( { 2 }^{ 3 } \div { 2 }^{ 5 } \right) }^{ 4 } \times { 2 }^{ -5 }$$

Evaluate

$$\frac{1}{8192}=0.00012207$$

Solution Steps

Rewrite 2^{5} as 2^{3}\times 2^{2}. Cancel out 2^{3} in both numerator and denominator.

$$\left(\frac{1}{2^{2}}\right)^{4}\times 2^{-5}$$

Calculate 2 to the power of 2 and get 4.

$$\left(\frac{1}{4}\right)^{4}\times 2^{-5}$$

Calculate \frac{1}{4} to the power of 4 and get \frac{1}{256}.

$$\frac{1}{256}\times 2^{-5}$$

Calculate 2 to the power of -5 and get \frac{1}{32}.

$$\frac{1}{256}\times \frac{1}{32}$$

Multiply \frac{1}{256} and \frac{1}{32} to get \frac{1}{8192}.

$$\frac{1}{8192}$$

Factor

$$\frac{1}{2 ^ {13}} = 0.0001220703125$$