Exponent question:?

Question

(25 a^6 b^8) ^1/2


how do i solve this??

and what happens to the 25??

Answer 1

Three rules apply here.
1. (pq)^r =(p^r) (q^r).
2. (p^q)^r = p^(q*r).
3. p^(a/b) = the b-th root of (p^a).

25^(1/2) becomes 5 .................. (rule 3)
(a^6)^(1/2) becomes a^(6*1/2) ........ (rule 2)
(b^8)^(1/2) .......... (rule 2 again).

Thus:
(25 a^6 b^8) ^(1/2)
= [25^(1/2)] * [(a^6)^(1/2)] * [(b^8)^(1/2)]
= 5 * a^(6*1/2) * b^(8*1/2)
= 5 a^3 b^4.

Answer 2

when you have a power to a power, multiply the exponents

(25 a^6 b^8)

= 25^(1/2) a^(6 * 1/2) b^(8*1/2)

= 5 a^3 b^4

Answer 3

You can break it down to:

25^.5 x (a^6)^.5 x (b^8)^.5 =
5 x a^3 x b^4 = (5 a^3 b^4)

Answer 4

The answer is 5a^3b^4. 25 to the power of 1/2is five. So 25 becomes 5

Answer 5

The question is asking you for the square root of the expression and once finding it you raise it to the first power

5 a^3 b^4 ^1= 5a^3 b^4