Solve [(-4)^{2}-3^{2}]^2+[(-3)^2-2^4]^2

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

Evaluate

$$98$$

Solution Steps

Calculate -4 to the power of 2 and get 16.

$$\left(16-3^{2}\right)^{2}+\left(\left(-3\right)^{2}-2^{4}\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$\left(16-9\right)^{2}+\left(\left(-3\right)^{2}-2^{4}\right)^{2}$$

Subtract 9 from 16 to get 7.

$$7^{2}+\left(\left(-3\right)^{2}-2^{4}\right)^{2}$$

Calculate 7 to the power of 2 and get 49.

$$49+\left(\left(-3\right)^{2}-2^{4}\right)^{2}$$

Calculate -3 to the power of 2 and get 9.

$$49+\left(9-2^{4}\right)^{2}$$

Calculate 2 to the power of 4 and get 16.

$$49+\left(9-16\right)^{2}$$

Subtract 16 from 9 to get -7.

$$49+\left(-7\right)^{2}$$

Calculate -7 to the power of 2 and get 49.

$$49+49$$

Add 49 and 49 to get 98.

$$98$$

Factor

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