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

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

Evaluate

$$441$$

Solution Steps

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

$$\left(8+\left(\frac{1}{3}\right)^{-2}+\left(\frac{1}{4}\right)^{-1}\right)^{2}$$

Calculate \frac{1}{3} to the power of -2 and get 9.

$$\left(8+9+\left(\frac{1}{4}\right)^{-1}\right)^{2}$$

Add 8 and 9 to get 17.

$$\left(17+\left(\frac{1}{4}\right)^{-1}\right)^{2}$$

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

$$\left(17+4\right)^{2}$$

Add 17 and 4 to get 21.

$$21^{2}$$

Calculate 21 to the power of 2 and get 441.

$$441$$

Factor

$$3^{2}\times 7^{2}$$