SOLUTION: Please help me with this problem Evaluate and express your answer with only positive exponent 1.(36 a^8b^10)^-1/2

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Question 251259: Please help me with this problem
Evaluate and express your answer with only positive exponent
1.(36 a^8b^10)^-1/2

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
equation is:

%2836%2Aa%5E8%2Ab%5E10%29%5E%28-1%2F2%29

* means multiplication

That is what I think your equation is.

rules of exponents you will use:

a%5E%28-b%29+=+1%2Fa%5Eb (rule 1)

(rule 2)

%28a%5Eb%29%5Ec+=+a%5E%28b%2Ac%29 (rule 3)

your equation of %2836%2Aa%5E8%2Ab%5E10%29%5E%28-1%2F2%29 becomes:

1%2F%2836%2Aa%5E8%2Ab%5E10%29%5E%281%2F2%29 by rule 1, which becomes:

1%2F%2836%5E%281%2F2%29%2A%28a%5E8%29%5E%281%2F2%29%2A%28b%5E10%29%5E%281%2F2%29%29 by rule 2, which becomes:

1%2F%28%2836%29%5E%281%2F2%29%2Aa%5E%288%2A%281%2F2%29%29%2Ab%5E%2810%2A%281%2F2%29%29%29 by rule 3, which becomes:

1%2F%286%2Aa%5E4%2Ab%5E5%29

a common mistake is to take something like %2836%2Aa%5E8%29%5E%281%2F2%29 and only work on a%5E8 and forgetting to work on 36 as well.

making this mistake, you would get %2836%2Aa%5E8%29%5E%281%2F2%29+=+%2836%2Aa%5E4%29.

not making this mistake, you woul get %2836%2Aa%5E8%29%5E%281%2F2%29+=+%286%2Aa%5E4%29.

that exterior exponent to the expression has to be applied to every term in the expression, including the coefficient of a term.

in the expression 36%2Aa%5E8, 36 is the coefficient of the term a%5E8. It is another term in the expression, just like a%5E8 is.

to prove your answer is correct, take any value for a and b and substitute for them in the original and final equation to see that you got the same answer.

let a = 3
let b = 6

use your calculator to solve.

original equation is:

%2836a%5E8%2Ab%5E10%29%5E%28-1%2F2%29 which becomes:

%2836%2A%283%29%5E8%2A%286%29%5E10%29%5E%28-1%2F2%29 which becomes:

.000000265

final equation is:

1%2F%286a%5E4%2Ab%5E5%29 which becomes

1%2F%286%2A%283%29%5E4%2A%286%29%5E5%29 which becomes:

.000000265

the answers are the same so the original equation has been simplified correctly.