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?