Simplify: $$S=3^{1/3}\cdot7^{1/4}$$
How is it possible to simplify this? The exponents are completely different.
2026-04-11 23:23:57.1775949837
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Simplify: $S=3^{1/3}\cdot 7^{1/4}$
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$3=7×(3/7)$ therfore $3^{1/3}=(3/7)^{1/3}*7^{1/3} $ therfore $3^{1/3}*7^{1/4} =(3/7)^{1/3}*7^{1/3} *7^{1/4} = (3/7)^{1/3}*7^{7/12} $
the final term still has two bases to two exponents but I find it a simplified form to work with. Simplification to one term to a power is impossible due to 3 and 7 are coprime. In fact they are simply prime.
it is impossible to simplify this (you wrote the reason).
only you can write this as $\sqrt[12]{3^4\cdot 7^3}$