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I have a literal equation that needs to be solved for: $$r_{a}$$

Here is the equation:

$$ \frac{ T_{a} }{ T_{b} } = \left( \frac{ r_{a} }{ r_{b} } \right)^\frac{3}{2} $$

The answer I was able to achieve was:

$$\frac{( T_{a} )^ \frac{2}{3}\,. r_{b} }{( T_{b} )^ \frac{2}{3} } = r_{a}$$

I originally believed my answer was correct but now a friend of mine is convinced it can be further simplified. Could anyone help me with this problem? Thanks in advance!

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1 Answer 1

up vote 2 down vote accepted

Your friend is correct in saying that it can be further simplified down. Remember that $(\frac{a}{b})^n=\frac{a^n}{b^n}$

So, the fully simplified answer would be:

$$r_b\cdot\left(\frac{T_a}{T_b}\right)^\frac{2}{3}=r_a$$

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I can't believe I overlooked such a basic thing! My head must be getting cloudy from all this math. Thanks! –  ProfessorStealth Jan 25 at 23:28
    
Not a problem. I find it kind of strange how you had to have expanded that out to get your answer, but didn't notice it. –  Richard P Jan 25 at 23:38
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