2(-2)^4+3(-2)^3+2 times(-2)+3(-2)+6

To solve the expression \( 2(-2)^{4}+3(-2)^{3}+2 \times(-2)+3(-2)+6 \), we need to evaluate each term step by step:<br /><br />1. Calculate \((-2)^4\):<br /> \[<br /> (-2)^4 = (-2) \times (-2) \times (-2) \times (-2) = 16<br /> \]<br /><br />2. Calculate \(2(-2)^4\):<br /> \[<br /> 2 \times 16 = 32<br /> \]<br /><br />3. Calculate \((-2)^3\):<br /> \[<br /> (-2)^3 = (-2) \times (-2) \times (-2) = -8<br /> \]<br /><br />4. Calculate \(3(-2)^3\):<br /> \[<br /> 3 \times (-8) = -24<br /> \]<br /><br />5. Calculate \(2 \times (-2)\):<br /> \[<br /> 2 \times (-2) = -4<br /> \]<br /><br />6. Calculate \(3(-2)\):<br /> \[<br /> 3 \times (-2) = -6<br /> \]<br /><br />Now, substitute these values back into the original expression:<br />\[<br />32 + (-24) + (-4) + (-6) + 6<br />\]<br /><br />Combine the terms:<br />\[<br />32 - 24 - 4 - 6 + 6<br />\]<br /><br />Simplify step by step:<br />- \(32 - 24 = 8\)<br />- \(8 - 4 = 4\)<br />- \(4 - 6 = -2\)<br />- \(-2 + 6 = 4\)<br /><br />Thus, the value of the expression is \(\boxed{4}\).