Question

(13)raise to √x =4 raised to 4 -3 raise to 4 -6

Answer 1

Step-by-step explanation:

Positive and Negative Exponents

Date: 07/27/97 at 14:26:29

From: Anonymous

Subject: Exponents

Dr. Math,

Could you please explain why (-1)^n = 1 for any even number n, and why

(-17)^-8 is positive?

Thank you for your help,

BradyRed

Date: 07/28/97 at 13:21:43

From: Doctor Beth

Subject: Re: Exponents

Good question! The general idea of raising a number to a positive

integer exponent "n" is to multiply that number by itself n times; for

example, (-1)^4 = (-1)*(-1)*(-1)*(-1) = 1. Remember that two

negatives multiply to be a positive, so that if "n" is even, all the

negatives can be paired with another negative, and the result is

positive. So that's why any number to an even positive power is

positive. (Incidentally, that's why you can't find a real number that

is the even root of a negative number; for example, there is no real

number that is the square root of -1, because to be the square root

of -1, the number squared would have to be -1, which we just decided

can't happen.)

Now for your second question. Negative exponents are a bit tricky at

first - they mean that you have to put the number in the denominator

and take a positive exponent. In symbols, this is the same as saying

that

1

a^(-b) = ----- .

a^b

So (-17)^(-8) = 1/(-17)^8, and since 8 is even, (-17)^8 is positive,

so that 1/(-17)^8 is positive.

Thanks for the question!