Question 405948
Thisis how I read what you posted:
<br>{{{3^((root(3, m^11/64)))-(4m^3)^((root(3, m^2/27)))}}}
If this is not what you meant then repost your problem with<ul><li>Precise wording. Make you you are using the correct words to describe your expression.</li><li>Parentheses around<ul><li>Numerators</li><li>Denominators</li><li>Exponents</li><li>Radicands (the expressions inside a radical)</li></ul></li></ul>
In case the expression above is correct, then the only simplification that can be done is with the 3rd (aka cube) roots. Rewriting the radicands with perfect cube factors we get:
<br>{{{3^((root(3, (m^3*m^3*m^2*m^2)/4^3)))-(4m^3)^((root(3, m^2/3^3)))}}}
Using the following properties of radicals, {{{root(a, p*q) = root(a, p)*root(3, q)}}} and {{{root(a, p/q) = root(a, p)/root(3, q)}}}, we can split off the perfect cube factors into their own cube roots:
<br>{{{3^((root(3, (m^3)*root(3, m^3)*root(3, m^3)*root(3, m^2))/root(3, 4^3)))-(4m^3)^((root(3, m^2)/root(3, 3^3)))}}}
The cube roots of the perfect cubes simplify:
<br>{{{3^(((m*m*m*root(3, m^2))/4))-(4m^3)^((root(3, m^2)/3))}}}
which simplifies to:
<br>{{{3^(((m^3*root(3, m^2))/4))-(4m^3)^((root(3, m^2)/3))}}}
This is far as we can go (as far as I can tell.)