## Need help on this Simplification of ALgebra

Simplificatation, evaluation, linear equations, linear graphs, linear inequalities, basic word problems, etc.
cls
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### Need help on this Simplification of ALgebra

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
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Joined: Mon Dec 08, 2008 4:22 pm
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cls wrote: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
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Joined: Fri Jan 13, 2012 5:22 pm
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### Re: Need help on this Simplification of ALgebra

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.

cls
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Joined: Fri Jan 13, 2012 5:22 pm
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### Re: Need help on this Simplification of ALgebra

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

stapel_eliz
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Joined: Mon Dec 08, 2008 4:22 pm
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cls wrote: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.

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:

. . . . .$\left(\frac{R^2}{4}\right) \left(3x\right)^R \left(\frac{2}{9x^2}\right)^{6-R}$

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 xR divided by (x2)6-R simplify to x3. What can you learn about R from this?

And so forth.

cls
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Joined: Fri Jan 13, 2012 5:22 pm
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### Re: Need help on this Simplification of ALgebra

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 !!!