positive and neg. exponents when multiplied?

Question

(3a^-1)^-1
why does this -1 times -1 equal a negative one?
yet on another problem i had -3 times -4 equal positive 12
...this is for a greater probelm....(3a^-1)-1 (9a^2 b^3)^-2
OVER
(3^3 a^-3 b^6_ ^-4

Answer 1

Exponents don't multiply together the same way base numbers do. When exponents are multiplied together, the exponents add. For example:

2 * 3 = 6, but
x^2 * x^3 = x^5

(you can prove this to yourself -- let x equal 5. 5^2 is 25, and 5^3 is 125, and 25 ^ 125 is 3125 which is the same as 5^5)

However, the question as stated isn't about multiplying exponents, it is about simplifying exponents. Lets look at it that way:

x^-1 also means 1/x if it helps to think of it that way (and X^-2 means 1/X^2, and so on). You can use this fact in simplifying exponents within an expression.

So, using that fact and the mathematical order of operations (remember PEMDAS -- Parenthesis, Exponents, Multiplication and Division, then Addition and Subtraction), the term (3a^-1)^-1 simplifies as follows:

. (3a^-1)^-1 --- starting form, isolate the first exponent:
. (3 * a^-1)^-1 --- convert negative exponent to 1/x form:
. (3 * 1/a^1)^-1 --- x^1 equals x, so simplify:
. (3 * 1/a)^-1 --- simplify the parentheses:
. (3/a)^-1 --- convert negative exponent to 1/x form:
. 1/(3/a) --- invert the fraction in the denominator:
. a/3 --- and finally express in exponents:
. a * 3^-1

Answer 2

When exponents are raised to another exponent, the exponents multiply in the usual manner, I.e. a negative times a negative give a positive. There is nothing special. As other responders have shown, (3a^-1)^-1 = 3a [or (3a)^+1]; in other words, the -1 times -1 gives +1 in the exponent.

Answer 3

o.k for the 1st question u will have
(3a^-1)^-1= 3^-1*a^1=a/3 why?
because the exponent here must be multiplied with the other and so posative exponent multiplied with negative exponent the answer must be negative and thats: (3^+1)^-1=3^-1also when we multiplied a negative exponent with negative exponent we get posative exponent as : (a^-1)^-1

and for the 2nd puzzle i believe that you have some thing wrong because -1*-1=+1 (because of this rule -a times -b=+ab)

and for the 3rd puzzle the same thing -3*-4=+12(-a*-b=+ab)

and iam sorry i cant help u with the last one because its long and i dont have enough time so good bye and good luck and believe me its the right answers

Answer 4

(3a^-1)^-1

first thing you to do turn the negative exponent positive is to move it to the denominator of a fraction....

__1____ =
(3a^-1)^1

___1__
3a^-1

This leaves you with a negative in the denominator again, so you do the same thing, place a 1 over it and remove the negative sign,

__1____
_1__
3a^1

what your fraction really is, is this 1/1 divided by 1/3a^1

how do you divide, you multiply by the reciprocal

1/1 x 3a^1/1 = 3a^1/1 = 3a^1

oh, and when you multiply exponents, you multiply the integers, but you add the exponent, you don't multiply it. for example

y^2 x y^3 = y^5

Answer 5

(3a^-1)^-1=3a^(-1)(-1)=3a ^1 same rule (-1)(-1)=+1
3a^-1)^-1(9a^2b^3)^-2
=3a/9a^2b^3=1/3ab^3