Solve 400-5*{32+(-2)*[18-2*(16-(-2)^4)]}+(-5)^4*(-5)^2=

$$400 - 5 \cdot \{ 32 + ( - 2 ) \cdot [ 18 - 2 \cdot ( 16 - ( - 2 ) ^ { 4 } ) ] \} + ( - 5 ) ^ { 4 } \cdot ( - 5 ) ^ { 2 } =$$

Evaluate

$$16045$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$400-5\left(32-2\left(18-2\left(16-\left(-2\right)^{4}\right)\right)\right)+\left(-5\right)^{6}$$

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

$$400-5\left(32-2\left(18-2\left(16-16\right)\right)\right)+\left(-5\right)^{6}$$

Subtract 16 from 16 to get 0.

$$400-5\left(32-2\left(18-2\times 0\right)\right)+\left(-5\right)^{6}$$

Multiply 2 and 0 to get 0.

$$400-5\left(32-2\left(18-0\right)\right)+\left(-5\right)^{6}$$

Subtract 0 from 18 to get 18.

$$400-5\left(32-2\times 18\right)+\left(-5\right)^{6}$$

Multiply -2 and 18 to get -36.

$$400-5\left(32-36\right)+\left(-5\right)^{6}$$

Subtract 36 from 32 to get -4.

$$400-5\left(-4\right)+\left(-5\right)^{6}$$

Multiply 5 and -4 to get -20.

$$400-\left(-20\right)+\left(-5\right)^{6}$$

The opposite of -20 is 20.

$$400+20+\left(-5\right)^{6}$$

Add 400 and 20 to get 420.

$$420+\left(-5\right)^{6}$$

Calculate -5 to the power of 6 and get 15625.

$$420+15625$$

Add 420 and 15625 to get 16045.

$$16045$$

Factor

$$5\times 3209$$