What is the difference between 5^ 8 and 5^ -8?

Question

Please explain all steps taken.

Answer 1

5^8 = 5*5*5*5*5*5*5*5 = 390625
5^(-8) = 1/(5^8) = 0.00000256

Answer 2

I think...

5^8 = 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5

and

5^-8 = 1 / (5 x 5 x 5 x 5 x 5 x 5 x 5 x 5)

Answer 3

5^8 = 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 = 390,625

The negative sign in an exponent means that the equation goes UNDER a fraction sign -- so :

5^-8 really = 1/5^8 or 1/390,625 or 0.00000256

Anytime you have a negative exponent, turn the problem around so that the exponent is positive, but under a fraction.

Answer 4

5^8 = 39625
5^-8 = 1/39625 = 0.00002537

39625 - 0.00002537 = 39624.99997463

Answer 5

5^8 = 5*5*5*5*5*5*5*5 = 390625
5^(-8) = 1/(5^8) = 0.00000256
5^8 - 5(-8) = 390624.99999744

Answer 6

A negative exponent always denotes that expression is in the denominator. So by putting it in the denominator, the exponent then becomes positive.
Therefore, (anything) ^ (a negative exponent) is really
1/(anything)^(that same exponent but now it's positive)

So if 5^8 = 390625, then 5^-8 is 1/(5^8) = 1 / 390625

=) Hope that wasn't too entirely confusing lol

Answer 7

5^8 = 390,625 whilst 5^-8 is 0.0000128. I could be wrong, but since my calculator doesn't have a ^ button I did 5/5 8 times as opposed to 5x5 8 times. A negative power results in a decimal.
Hope that helps. =)

Answer 8

5^8 means 5*5*5*5*5*5*5*5
5^-8 means 1/(5*5*5*5*5*5*5*5)
they are reciprocals of one another