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]
To solve these problems, we'll follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right). Let's start with the first problem:
Problem 1: 12^2 + 2[(13+3)] / 2^2
Step 1: Inside the parentheses, we have 13 + 3, which simplifies to 16.
12^2 + 2[16] / 2^2
Step 2: Next, we focus on the exponentiation. 12^2 means 12 raised to the power of 2, which is 144.
144 + 2[16] / 2^2
Step 3: Now, we need to multiply 2 by 16, which gives us 32.
144 + 32 / 2^2
Step 4: Next, we evaluate 2^2, which is 4.
144 + 32 / 4
Step 5: Finally, we perform the division. 32 divided by 4 is equal to 8.
144 + 8
Therefore, the final answer is 152.
Moving on to the second problem:
Problem 2: -4(3) + 5[7 - 6(-4)^2]
Step 1: Inside the parentheses, we have -4 multiplied by 3, which gives us -12.
-12 + 5[7 - 6(-4)^2]
Step 2: We need to evaluate the exponent first. (-4)^2 means -4 raised to the power of 2, which is 16.
-12 + 5[7 - 6(16)]
Step 3: Next, we perform the multiplication. -6 multiplied by 16 is -96.
-12 + 5[7 - 96]
Step 4: Inside the square brackets, we subtract 96 from 7, giving us -89.
-12 + 5[-89]
Step 5: Finally, we multiply 5 by -89, which is -445.
-12 + (-445)
To add a positive and a negative number, we subtract their absolute values and use the sign of the larger number.
-12 - 445
Therefore, the final answer is -457.
Now let's solve the third problem:
Problem 3: -5(3) + 3[9 - 6(-3)^2]
Step 1: Inside the parentheses, we have -5 multiplied by 3, which gives us -15.
-15 + 3[9 - 6(-3)^2]
Step 2: Let's evaluate the exponent first. (-3)^2 means -3 raised to the power of 2, which is 9.
-15 + 3[9 - 6(9)]
Step 3: Performing the multiplication, we get -6 multiplied by 9, which is -54.
-15 + 3[9 - 54]
Step 4: Inside the square brackets, we subtract 54 from 9, resulting in -45.
-15 + 3[-45]
Step 5: Finally, we multiply 3 by -45, giving us -135.
-15 - 135
Adding a negative number is the same as subtracting its absolute value.
-15 - 135
Therefore, the final answer is -150.
I hope this explanation helps you solve these problems! Let me know if you have any further questions.