Question: User: $n^{5/4} \times n^{2/3}$
1. **State the problem:** Simplify the expression $$n^{5/4} \times n^{2/3}$$.
2. **Recall the rule for multiplying powers with the same base:** When multiplying expressions with the same base, add the exponents: $$a^m \times a^n = a^{m+n}$$.
3. **Apply the rule:**
$$n^{5/4} \times n^{2/3} = n^{5/4 + 2/3}$$
4. **Find a common denominator to add the exponents:**
The denominators are 4 and 3. The least common denominator is 12.
Convert each exponent:
$$\frac{5}{4} = \frac{5 \times 3}{4 \times 3} = \frac{15}{12}$$
$$\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}$$
5. **Add the exponents:**
$$\frac{15}{12} + \frac{8}{12} = \frac{23}{12}$$
6. **Write the simplified expression:**
$$n^{23/12}$$
**Final answer:** $$n^{23/12}$$