math help simplify exponents?

Question

(x^(2/3)*y^(-3/4))^(12/3)

^ =power of

Answer 1

(a^b * c^d)^e = a^be * c^de

12/3 is 4

So you have this: x^(2/3)4 * y^(-3/4)4

In the first case the exponen is 8/3, this means the 3rd root of x^8. In the second case the exponent is -3, this means 1/(y^3)

Later

Ana

Answer 2

OK. So when you raise a power to a power, you multiply the exponents... so.

(x^(2/3)*y^(-3/4))^(12/3) ... 12/3 is the same as 4/4 or just 4

so... multiply 4 by each exp of x and y

(x^(2/3)(4)*y^(-3/4)(4))
= x^(8/3) * y^ (-3) which could also be written as...
= x^(8/3) * (1/ y^3)

Answer 3

First 12/3 = 4
(x^(2/3)*y^(-3/4))^(12/3)
= (x^(2/3)*y^(-3/4))^(4)
Next multiply exponents.
x^(2/3 *4)y^(-3/4 *4)
= x^(8/3)y^(-3)
= x^(8/3)/y^3
Note: x^(8/3) means the third root of x^8

Answer 4

There are 3 straightforward regulations x^a*x^b = x^(a+b) x^a/x^b = x^(a-b) (x^a)^b = x^(ab) so on your 2d get at the same time 9a^13 / a^3 = 9^(13-3) = 9a^10 Taking one further down (2a^4 b)^3 =2^3a^12b^3 =8a^12b^3

Answer 5

take the first three exponents and erase them with your alt-ctl-del buttons down and then remove the remaining fractions with a paste and cut and you will simplify everything

Answer 6

(x^(2/3) * y^(-3/4)) ^ (1 2/3)

(x^(2/3) * y^(-3/4)) ^ (5/3)

x^[(2/3)*(5/3)] * y^[(-3/4)*(5/3)]

x^(10/3) * y^(-5/4)

4y^(5/4) * x^(10/3) / y^5

Answer 7

(x^(2/3) * y^(-3/4))^(12/3)
(x^(2/3) * y^(-3/4))^4

x^((2/3) * 4) * y^((-3/4) * 4)

x^(8/3) * y^(-3)

ANS : (x^(8/3))/(y^3)