Solve 2^{-5}+(1/2)^-4+2^-1*2^-3*2+(pi-3.14)^0

$$2 ^ { - 5 } + ( \frac { 1 } { 2 } ) ^ { - 4 } + 2 ^ { - 1 } \times 2 ^ { - 3 } \times 2 + ( \pi - 3.14 ) ^ { 0 }$$

Evaluate

$$17.15625$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -1 and -3 to get -4.

$$2^{-5}+\left(\frac{1}{2}\right)^{-4}+2^{-4}\times 2+\left(\pi -3.14\right)^{0}$$

To multiply powers of the same base, add their exponents. Add -4 and 1 to get -3.

$$2^{-5}+\left(\frac{1}{2}\right)^{-4}+2^{-3}+\left(\pi -3.14\right)^{0}$$

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

$$\frac{1}{32}+\left(\frac{1}{2}\right)^{-4}+2^{-3}+\left(\pi -3.14\right)^{0}$$

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

$$\frac{1}{32}+16+2^{-3}+\left(\pi -3.14\right)^{0}$$

Add \frac{1}{32} and 16 to get \frac{513}{32}.

$$\frac{513}{32}+2^{-3}+\left(\pi -3.14\right)^{0}$$

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

$$\frac{513}{32}+\frac{1}{8}+\left(\pi -3.14\right)^{0}$$

Add \frac{513}{32} and \frac{1}{8} to get \frac{517}{32}.

$$\frac{517}{32}+\left(\pi -3.14\right)^{0}$$

Calculate \pi -3.14 to the power of 0 and get 1.

$$\frac{517}{32}+1$$

Add \frac{517}{32} and 1 to get \frac{549}{32}.

$$\frac{549}{32}$$

Factor

$$\frac{61 \cdot 3 ^ {2}}{2 ^ {5}} = 17\frac{5}{32} = 17.15625$$