Review question

When is this product of powers an integer? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6983

Suggestion

Let $r$ and $s$ be integers. Then $\frac{6^{r+s}\times12^{r-s}}{8^r\times9^{r+2s}}$ is an integer if

1. $r+s\le 0$,

2. $s \le 0$,

3. $r\le 0$,

4. $r\ge s$.

Maybe we could break $6, 12, 8$ and $9$ down into their prime factors to rewrite the expression?