Solve [(3^{-7}+2^-7)^-1+(1/2)^-2]^-2

$$[ ( 3 ^ { - 7 } + 2 ^ { - 7 } ) ^ { - 1 } + ( \frac { 1 } { 2 } ) ^ { - 2 } ] ^ { - 2 }$$

Evaluate

$$\frac{5359225}{83634326416}\approx 0.000064079$$

Solution Steps

Calculate 3 to the power of -7 and get \frac{1}{2187}.

$$\left(\left(\frac{1}{2187}+2^{-7}\right)^{-1}+\left(\frac{1}{2}\right)^{-2}\right)^{-2}$$

Calculate 2 to the power of -7 and get \frac{1}{128}.

$$\left(\left(\frac{1}{2187}+\frac{1}{128}\right)^{-1}+\left(\frac{1}{2}\right)^{-2}\right)^{-2}$$

Add \frac{1}{2187} and \frac{1}{128} to get \frac{2315}{279936}.

$$\left(\left(\frac{2315}{279936}\right)^{-1}+\left(\frac{1}{2}\right)^{-2}\right)^{-2}$$

Calculate \frac{2315}{279936} to the power of -1 and get \frac{279936}{2315}.

$$\left(\frac{279936}{2315}+\left(\frac{1}{2}\right)^{-2}\right)^{-2}$$

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

$$\left(\frac{279936}{2315}+4\right)^{-2}$$

Add \frac{279936}{2315} and 4 to get \frac{289196}{2315}.

$$\left(\frac{289196}{2315}\right)^{-2}$$

Calculate \frac{289196}{2315} to the power of -2 and get \frac{5359225}{83634326416}.

$$\frac{5359225}{83634326416}$$

Factor

$$\frac{5 ^ {2} \cdot 463 ^ {2}}{2 ^ {4} \cdot 197 ^ {2} \cdot 367 ^ {2}} = 6.407925106424641 \times 10^{-5}$$