i need help with school homework

Question

i need help with algebra 1 exponents and Oder of Operations 

Answer 1

A good mnemonic is Please Excuse Me Dear Aunt Sally.

 

Please stands for Parenthesis: do what's in them first.

 

Excuse stands for Exponents: do these next.

 

Me stands for Multiplication: do these next.

 

Aunt stands for Addition: do these next.

 

Sally stands for Subtraction: do these last.

Answer 2

5 * (7 + 2)    parentheses
3²    exponents
6 * 7 / 3 * 4     multiplication/division
3 - 7 - 1 + 4 - 2    addition/subtraction

 

Parentheses are often used to use lower operational order higher up on the list. That way, you can add or subtract before you multiply or use an exponent, for example.

 

Exponents are a form of multiplication (3² = 3 * 3, after all); we happen to give it priority as the exponents tend to focus on a particular number, and they get used on variables a lot.

 

Multiplication and division hold the same ranking, so if a string of numbers in an area have cancellations, we can do that before we move onto the lowest order.

 

Once we've done all of the above, we can finally add or subtract the numbers together for the final answer.

 

Example:

10 + 6(3 + 5)² / 4 - 25

By order of operations, we have to look at the parentheses first:

3 + 5 = 8

So:

10 + 6 * 8² / 4 - 25 / 5

 

Next is exponents:

8² = 64

So:

10 + 6 * 64 / 4 - 25 / 5

 

Next we have multiplication and division. Take note, that we have a minus sign in the middle of some of them, so that means we have to treat that as a break into separate sections:

6 * 64 / 4

We can go straight across, but since they share the same operational order, we can make it a little easier by dividing the 64/4 first and then move onto the multiplying by 6:

64 / 4 = 16

6 * 16 = 96

We also have a division set at the end to look at:

-25 / 5 = -5

So:

10 + 96 - 5

 

Finally, we have addition and subtraction. Like mult/div, if we see a way to reorder like things to more easily cancel out, then we can use that. Not really the case here, but just to show you what I mean about reordering:

10 - 5 = 5

96 + 5 = 101

Similarly:

96 + 10 = 106

106 - 5 = 101

 

So our final answer is 101.

I hope this step-by-step walkthrough helps you to see how important the order of operations is and how to go through them.