# Solve a Literal Equation for a Specific Variable

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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Your friend is correct in saying that it can be further simplified down. Remember that $(\frac{a}{b})^n=\frac{a^n}{b^n}$
$$r_b\cdot\left(\frac{T_a}{T_b}\right)^\frac{2}{3}=r_a$$