simplify the following problems. show all work
1) -1[-2(-3)^3]^2
2) -3{3-2{10-3(-2)^2}^2]^2
3) -3[4-7(-3-5)]-(-5)^2
Sure, I can help you simplify these expressions! Let's solve them step by step and show all the work.
1) -1[-2(-3)^3]^2
First, let's simplify the expression inside the innermost parentheses: (-3)^3 = -3 * -3 * -3 = -27.
Next, we substitute the value we obtained into the equation: -1[-2(-27)]^2.
Next, we simplify inside the next set of parentheses: -2 * -27 = 54.
Now we substitute the value we obtained: -1[54]^2.
Next, we simplify inside the brackets: -1 * 54^2.
Now, we square 54: 54^2 = 54 * 54 = 2,916.
Finally, we substitute the value we obtained: -1 * 2,916 = -2,916.
Therefore, the simplified value is -2,916.
2) -3{3-2{10-3(-2)^2}^2}^2
First, let's simplify the expression inside the innermost parentheses: (-2)^2 = 4.
Next, we substitute the value we obtained into the equation: 10 - 3 * 4 = 10 - 12 = -2.
Next, we simplify inside the next set of braces: 3 - 2 * (-2) = 3 + 4 = 7.
Now we substitute the value we obtained: -3{7}^2.
Next, we square 7: 7^2 = 7 * 7 = 49.
Finally, we substitute the value we obtained: -3 * 49 = -147.
Therefore, the simplified value is -147.
3) -3[4-7(-3-5)]-(-5)^2
First, let's simplify the expression inside the inner parentheses: -3 - 5 = -8.
Next, we substitute the value we obtained into the equation: -3[4 - 7(-8)] - (-5)^2.
Next, we simplify inside the brackets: -7 * (-8) = 56.
Now we substitute the value we obtained: -3[4 + 56] - (-5)^2.
Next, we simplify inside the next set of brackets: 4 + 56 = 60.
Now we substitute the value we obtained: -3 * 60 - (-5)^2.
Next, we square -5: (-5)^2 = (-5) * (-5) = 25.
Finally, we substitute the value we obtained: -3 * 60 - 25 = -180 - 25 = -205.
Therefore, the simplified value is -205.