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help me solve 8 divided 2.2 - 3 to the 2nd power

Today i went to class and was given another sheet with 33 more problems on them, I recieved a 85% on my homework....these last seven questions has me stuck again can anyone out there help me by not just given me the answers but helping me explain the problem of how I got the answers

 

thank you

Janice

 

Problem 1.  Simplify 8 divided by 2 times 2 minus 3 to the 2nd power

Problem 2.  simplify -4 + 2 3rd power / 4 - 3. 2

Problem 3. simplify 5 - 3 . 4 to the 2nd power + 3(-4 - (-6)

Problem 4. if X = -3 then 4X to the second power - 3x - 10 =

Problem 5. A 8 foot board is cut into two pieces. One piece is 2 feet longer than the other. How long is the smaller piece?

Problem 6. Simplify (3x to the 2nd power y)( 2x to the 3rd power y )

Problem 7. simplify the  expression 5a to the 3rd power - 2a to the 2nd power -( 4a to the 2nd power - 3 ) I came up with  5a to the 3rd power - 6a to the 2nd power - 3 for my answer am i right?

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2 Answers

Problems 1, 2, and 3: I'm not sure I can rewrite these correctly, so I'll answer generally. It looks like each of these involve the order of operations, which is: 

Parentheses, Exponents, Multiplication/Division (from left to right), Addition/Subtraction (from left to right).

So if problem 1 is 8 divided by 2 times 2 minus 3 to the 2nd power

this would look like 8 ÷ 2 * 2 - 32

By order of operations, we do the exponents (32) first, and we get

8 ÷ 2 * 2 - 9

Now we do multiplication and division as we encounter them from left to right. So first we tackle 8 ÷ 2 and rewrite our expression with the result

4 * 2 - 9

Now we have 4 * 2 (which equals 8), and we rewrite our expression again:

8 - 9

Now, there is nothing left but subtraction, and 8-9 = -1. 

Given that explanation, see if you can apply this process to problems 2 and 3

You can remember the order of operations with the saying "Please Excuse My Dear Aunt Sally":
Please = Parentheses
Excuse = Exponents
My = Multiplication
Dear = Division
Aunt = Addition
Sally = Subtraction

Problem 4: If x = -3, then 4x2 - 3x - 10 = ?

Replace x in the expression with (-3), to get

4(-3)2 - 3(-3) - 10 = 4(9) + 9 - 10 = (I'll leave the final answer for you)

Problem 5: Since the board is cut into two pieces, let's let x  = length of first piece and y = length of second piece. We then know that x + y = 8 feet 

Since one piece is 2 feet longer than the other, let's assume that the first piece is longer than the second, so we now have a second equation,  x = y + 2

Replace x in the first equation with y+2 (from the second equation), and we now have

(y+2) + y = 8

2y + 2 = 8

2y = 6

y = 3 . Since we assumed that y was the shorter board, this is our answer. 

Problem 6: I'm reading this as (3x2y)(2x3y). 

If so, we multiply common factors together:

(3*2)(x2x3)(yy) = 6 x2+3y1+1 = 6x5y2

 

Problem 7: If looks like the problem is 5a3 - 2a2 - (4a2 - 3). If so, then your answer is close, with one change: 

The negative in front of (4a2 - 3) gets distributed across both terms within the parentheses. So if we cleared the parens, our expression would look like 

5a3 - 2a2 + (-1)( 4a2) + (-1)(- 3) = 5a3 - 6a2 +  3