Solve -5(-3-2)^2(-4+1)^2(-1-3)^4<0

$$- 5 ( - 3 - 2 ) ^ { 2 } ( - 4 + 1 ) ^ { 2 } ( - 1 - 3 ) ^ { 4 } < 0$$

Verify

Solution Steps

Subtract 2 from -3 to get -5.

$$-5\left(-5\right)^{2}\left(-4+1\right)^{2}\left(-1-3\right)^{4}<0$$

Calculate -5 to the power of 2 and get 25.

$$-5\times 25\left(-4+1\right)^{2}\left(-1-3\right)^{4}<0$$

Multiply -5 and 25 to get -125.

$$-125\left(-4+1\right)^{2}\left(-1-3\right)^{4}<0$$

Add -4 and 1 to get -3.

$$-125\left(-3\right)^{2}\left(-1-3\right)^{4}<0$$

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

$$-125\times 9\left(-1-3\right)^{4}<0$$

Multiply -125 and 9 to get -1125.

$$-1125\left(-1-3\right)^{4}<0$$

Subtract 3 from -1 to get -4.

$$-1125\left(-4\right)^{4}<0$$

Calculate -4 to the power of 4 and get 256.

$$-1125\times 256<0$$

Multiply -1125 and 256 to get -288000.

$$-288000<0$$

Compare -288000 and 0.

$$\text{true}$$