Solve (-1/2)^-2+(1/3)^-3+(1/4)^-4

$$( \frac { - 1 } { 2 } ) ^ { - 2 } + ( \frac { 1 } { 3 } ) ^ { - 3 } + ( \frac { 1 } { 4 } ) ^ { - 4 }$$

Evaluate

$$287$$

Solution Steps

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

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

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

$$4+\left(\frac{1}{3}\right)^{-3}+\left(\frac{1}{4}\right)^{-4}$$

Calculate \frac{1}{3} to the power of -3 and get 27.

$$4+27+\left(\frac{1}{4}\right)^{-4}$$

Add 4 and 27 to get 31.

$$31+\left(\frac{1}{4}\right)^{-4}$$

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

$$31+256$$

Add 31 and 256 to get 287.

$$287$$

Factor

$$7\times 41$$