simplify (9a^6b^2)^-1/2?

Answer 1

When you have a power which is negative, it means 1 divided by the 'stuff to the positive power'
eg. (9(a^6)(b^2))^(-1/2) = 1/((9(a^6)(b^2))^(1/2))

The power is a fraction. This means that the 'stuff' being raised to the power 1/n should have it's nth root taken.
eg. (9(a^6)(b^2))^(1/2) = sqrt(9(a^6)(b^2))

Therefore:
1/((9(a^6)(b^2))^(1/2)) = 1/sqrt(9(a^6)(b^2))

Therefore the answer is:
(9(a^6)(b^2))^(-1/2) = 1/(3b(a^3)) = (3b(a^3))^(-1)

However, instead of doing it this way, the same answer can be achieved through multiplying the powers of 9(a^6)(b^2) by the power you are raising it to.
eg. The rule ((a^b)(c^d))^e = (a^be)(c^de)

And then using the above rules about negative and fractional powers to solve the problem.

Hope this isn't confusing...

Answer 2

that's all about searching elementary denominator. a million/2 = 4/8 -- 4/8 + a million/8 = 5/8 5/8 = 10/16 -- 10/16 + 5/16 = 15/16 a million/3 = 3/9 -- a million/9 + 3/9 = 4/9 a million/15 = 4/60 5/12 = 25/60 -- 4/60 + 25/60 = 29/60 i don't think of that those may be simplified any more beneficial than that. desire this facilitates.

Answer 3

Any negative exponent can be made positive by putting 1 over the expression.

9(a^6)(b^2)^(-1/2) =

1/ [9(a^6)(b^2)]^(1/2)

All you have to do is take the square root of each term individually (since taking something to the 1/2 is the same as taking the square root)
1 / [3(a^3)(b)]

Answer 4

(9a^6b²)^-1/2 = 1 / (3a³b)
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Answer 5

Hello :)

1 / √(9 * a^6 * b^2)
= 1 / √[3^2 * (a^3)^2 * b^2]
= 1 / [3 * a^3 * b]

Hope it helps :)

Answer 6

( 9 x a exp 6 x b exp 2) exp -1/2
[(3 exp 2) x a exp (2x3) x b exp 2] exp -1/2
3 x a exp 3 x b
3ba^3

Answer 7

[9 a^6 b^2]^-1/2
=3a^3b

Answer 8

3a^3b

Answer 9

.333333b^-1a^-3

Answer 10

algebra = rubbish.