Exponents Help - 8th grade Math

[AbhiKap]

Hello people,

So I was just practicing some math when I came across this question: What is the exponential form of -5 * -5 * -5 * -5?

There are two answers that I think could be correct: (-5)^4 and -5^4

What exactly is the difference between the two?

Thanks!

 

[srmichael]

Hello people,

So I was just practicing some math when I came across this question: What is the exponential form of -5 * -5 * -5 * -5?

There are two answers that I think could be correct: (-5)^4 and -5^4

What exactly is the difference between the two?

Thanks!

(-5)^4 = (-5)(-5)(-5)(-5) = 625

-5^4 = -(5)(5)(5)(5) = -625

It is very important that you understand the differences between these as this tends to trip up a lot of students. Good question!

 

[HallsofIvy]

The distinction is "order of operations": "Please Excuse My Dear Aunt Sally". First do anything in parentheses, the exponents, then multiply or divide, then add and subtract. With \(\displaystyle (-5)^4\) you do the "-1" times "5" and then to the fourth power: (-5)(-5)(-5)(-5)= 625 since -1 to the fourth power is 1. With -5^4 you do the power first then the "-1": (-1)[(5)(5)(5)(5)]= -625