Solve 1(2^5div2^8)^5*2^-5

$$1 ( 2 ^ { 5 } \div 2 ^ { 8 } ) ^ { 5 } \times 2 ^ { - 5 }$$

Evaluate

$$\frac{1}{1048576}\approx 0.000000954$$

Solution Steps

Rewrite 2^{8} as 2^{5}\times 2^{3}. Cancel out 2^{5} in both numerator and denominator.

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

Calculate 2 to the power of 3 and get 8.

$$1\times \left(\frac{1}{8}\right)^{5}\times 2^{-5}$$

Calculate \frac{1}{8} to the power of 5 and get \frac{1}{32768}.

$$1\times \frac{1}{32768}\times 2^{-5}$$

Multiply 1 and \frac{1}{32768} to get \frac{1}{32768}.

$$\frac{1}{32768}\times 2^{-5}$$

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

$$\frac{1}{32768}\times \frac{1}{32}$$

Multiply \frac{1}{32768} and \frac{1}{32} to get \frac{1}{1048576}.

$$\frac{1}{1048576}$$

Factor

$$\frac{1}{2 ^ {20}} = 9.5367431640625 \times 10^{-7}$$