Solve [6^{-1}-7^{-1}]^-1-[4^-1-5^-1]^-1

$$[ 6 ^ { - 1 } - 7 ^ { - 1 } ] ^ { - 1 } - [ 4 ^ { - 1 } - 5 ^ { - 1 } ] ^ { - 1 }$$

Evaluate

$$22$$

Solution Steps

Calculate 6 to the power of -1 and get \frac{1}{6}.

$$\left(\frac{1}{6}-7^{-1}\right)^{-1}-\left(4^{-1}-5^{-1}\right)^{-1}$$

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

$$\left(\frac{1}{6}-\frac{1}{7}\right)^{-1}-\left(4^{-1}-5^{-1}\right)^{-1}$$

Subtract \frac{1}{7} from \frac{1}{6} to get \frac{1}{42}.

$$\left(\frac{1}{42}\right)^{-1}-\left(4^{-1}-5^{-1}\right)^{-1}$$

Calculate \frac{1}{42} to the power of -1 and get 42.

$$42-\left(4^{-1}-5^{-1}\right)^{-1}$$

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

$$42-\left(\frac{1}{4}-5^{-1}\right)^{-1}$$

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

$$42-\left(\frac{1}{4}-\frac{1}{5}\right)^{-1}$$

Subtract \frac{1}{5} from \frac{1}{4} to get \frac{1}{20}.

$$42-\left(\frac{1}{20}\right)^{-1}$$

Calculate \frac{1}{20} to the power of -1 and get 20.

$$42-20$$

Subtract 20 from 42 to get 22.

$$22$$

Factor

$$2\times 11$$