Please help me solve these problems.
12^2+2 [(13+3)] / 2^2]
-4(3)+5[7-6(-4)^2]
-5(3)+3[9-6(-3)^2]
Certainly! Let's solve these problems step by step:
1. 12^2 + 2[(13 + 3)] / 2^2
To solve this problem, we'll follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction).
- First, let's simplify the expression inside parentheses: (13 + 3) = 16.
- Next, we'll calculate the exponent 12^2 = 144.
- Moving on to the multiplication inside the square brackets, 2 * 16 = 32.
- Finally, let's calculate the division 32 / 2^2 = 32 / 4 = 8.
Therefore, 12^2 + 2[(13 + 3)] / 2^2 = 144 + 8 = 152.
2. -4(3) + 5[7 - 6(-4)^2]
Again, we'll use PEMDAS to solve this problem.
- Let's begin by calculating the exponent (-4)^2 = 16.
- Next, multiply 6 by 16: 6 * 16 = 96.
- Moving on to the multiplication outside the square brackets, -4 * 3 = -12.
- Now, we simplify the expression inside the square brackets: 7 - 96 = -89.
- Finally, multiply 5 by -89: 5 * (-89) = -445.
Therefore, -4(3) + 5[7 - 6(-4)^2] = -12 + (-445) = -457.
3. -5(3) + 3[9 - 6(-3)^2]
Using PEMDAS, let's solve this problem step by step.
- First, calculate the exponent (-3)^2 = 9.
- Next, multiply 6 by 9: 6 * 9 = 54.
- Moving on to the multiplication outside the square brackets, -5 * 3 = -15.
- Now, let's simplify the expression inside the square brackets: 9 - 54 = -45.
- Finally, multiply 3 by -45: 3 * (-45) = -135.
Therefore, -5(3) + 3[9 - 6(-3)^2] = -15 + (-135) = -150.
So, the solutions to the given problems are:
1. 12^2 + 2[(13 + 3)] / 2^2 = 152
2. -4(3) + 5[7 - 6(-4)^2] = -457
3. -5(3) + 3[9 - 6(-3)^2] = -150