Need help on this Simplification of ALgebra

[cls]

the below is to be simplify to 2/3X^2 but i just can't get it -:(
(R^2)/4 * (3x)^R * (2/9x^2)^(6-R) = 2/3X^2 -- proof it (R is eventually eliminated- how ??)

main obstacles is i can't get rid of the ^R, pls help

[stapel_eliz]

the below is to be simplify to 2/3X^2 but i just can't get it -:(
(R^2)/4 * (3x)^R * (2/9x^2)^(6-R) = 2/3X^2 -- proof it (R is eventually eliminated- how ??)

main obstacles is i can't get rid of the ^R, pls help

Are you supposed to be "simplifying" something, solving the equation, or proving something? (I'm assuming that "proof it" means "Prove the statement" or something similar.) Also, are "x" and "X" different variables (as is standard in algebra), or is the "X" a typo for "x"? Are you given any information about R or x or any relationship between the two?

What topics have you studied recently in class? (These might be helpful in figuring out what techniques they're expecting you to use.)

Thank you!

[cls]

Hi, thank you for your reply--
x=X, sorry for the typo.

The recent topic learnt is Exponential Equation.
the complete question is as follow -

If (R^2)/4 * (3X)^R * (2/9X^2)^(6-R) can be simplified to K/X^3 , find the values of the constants R and K.

(answer R=3, K=2/3)

[cls]

we have not learn Logarithms, so i can only try to use method like isolating exponent etc, but no luck :<

[stapel_eliz]

The recent topic learnt is Exponential Equation.
the complete question is as follow -

If (R^2)/4 * (3X)^R * (2/9X^2)^(6-R) can be simplified to K/X^3 , find the values of the constants R and K.

(answer R=3, K=2/3)

Ah. That's a different thing entirely from what I'd thought was meant. But it gives us more to work with.

When you're not sure what to do, do whatever you know, and see if that leads anywhere helpful. In this case, you have:

. . . . .

We are given that this simplifies to K/x³. Since we have a power of R on x and a power of 6 - R on x^2, and since we have x³ in the answer, then it must be that x^R divided by (x²)^6-R simplify to x³. What can you learn about R from this?

And so forth.

[cls]

Thank you for the great help !!
so i work out as -
X^(R-2(6-R)) = X^-3
R-12+2R=-3
3R=9
R=3

and K can then be solved !!!