Advanced Question Using Fractions and Negative Exponents

MathStudent2011

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Jun 14, 2011
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I am having troubles trying to calculate ((1/2)(1+2x))^(-1/2).

The answer is 1/(2*sqrt[2x+1])

Can some one please tell me where im going wrong?

I start with (1/2)*(2x+1) = (2x+1/2)^(-1/2),

then have (2/2x+1)^(1/2),

then have sqrt [2/2x+1]^1,

then have sqrt[2]/sqrt[2x+1] = 1/sqrt[2x+1].

Where am I going wrong?
 
MathStudent2011 said:
I am having troubles trying to calculate ((1/2)(1+2x))^(-1/2).
The answer is 1/(2*sqrt[2x+1])
If that's the answer, then expression should be: (1/2)(1 + 2x)^(-1/2)
 
Sorry I made some typos. I get that your dividing the whole term by 2 rather than just the single integer. Is there anything else wrong with my methodology?
 


MathStudent2011 said:
The answer is 1/(2*sqrt[2x+1])

Then this exercise seems to be nothing more than: "Rewrite the expression (1/2)(1+2x)^(-1/2) in radical form."



Can some one please tell me where im going wrong?

Maybe you have not yet learned that the following two expressions are different forms of the same value (for all Real n > 0):

n^(1/2) = sqrt(n)

We call the expression on the lefthand side "exponential form" and on the righthand side "radical form".

Given one form, we can switch to the other.

Of course, you also need to know the meaning of a negative exponent.

n^(-1/2) = 1/sqrt(n)


Therefore, in your exercise, you need only switch the expression (1 + 2x)^(-1/2) to radical form and multiply the result by 1/2.

If the exercise involves anything else, you have not clearly posted it. 8-)

 
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