How to prove the exponent law with rational exponents by Induction

Question

May I know how to prove that $b^n \times b^m = b^{n+m}$ given that the exponents are now rational numbers instead of pure integers ?

Answer 1

Hint: Write $$ n = \frac pq\\ m = \frac{p'}q $$ and then use that: $$ b^n = (b^{\frac 1q})^p $$