Addition of numbers with same base but different exponents

Question

The problem itself is $(288\sqrt{3})^{1/5}+(288\sqrt{3})^{4/5}$. The answer is supposed to be of the form $a+b\sqrt{c}$, but I have no idea how to simplify it.

It will probably help to know that $288=2^5\cdot 3^2$. – Jared May 23 '13 at 23:03 — Jared, May 23 '13 at 23:03

score 2 · Answer 1 · answered May 23 '13 at 23:04

2

HINT: Note that $288\sqrt3=2^5\cdot3^{5/2}$, so the first term is simply $2\sqrt3$. Now what’s the second term?

answered May 23 '13 at 23:04

Brian M. Scott

616,228

@user79199: Yes: $\left(2\sqrt3\right)^4=2^4\cdot3^2=144$. – Brian M. Scott May 23 '13 at 23:10
OK. Thanks a lot. – user79199 May 23 '13 at 23:11
@user79199: You’re welcome. – Brian M. Scott May 23 '13 at 23:11

Addition of numbers with same base but different exponents

1 Answers1