Question

I don't really get this.
Question: Use the rules for exponents and roots to prove that 512^2/3 = 16^3/2

Answer 1

Do you mean a rigorous formal proof?

Answer 2

I don't really know. This is what the question was and I don't get it.

Answer 3

Do you understand how to use logarithms?

Answer 4

No

Answer 5

Ah, you will want to understand natural logarithms for this question, I can explain it.

Answer 6

\[y = \log_b x\]
\[x = b^y\]

Answer 7

If we take the natural logarithm of \[512^{\frac{2}{3}}\]

\[\frac{2}{3}\ln(512)\]

Answer 8

We can pull the exponent out

Answer 9

So, is that a cube root? That we ended up with?