Question: User: 4² × 2³ × 8² =
1. **State the problem:** Calculate the value of the expression $$4^2 \times 2^3 \times 8^2$$.
2. **Recall the base and exponent values:**
- $$4^2 = 4 \times 4$$
- $$2^3 = 2 \times 2 \times 2$$
- $$8^2 = 8 \times 8$$
3. **Express all bases as powers of 2:**
- $$4 = 2^2$$, so $$4^2 = (2^2)^2 = 2^{2 \times 2} = 2^4$$
- $$2^3$$ remains as is.
- $$8 = 2^3$$, so $$8^2 = (2^3)^2 = 2^{3 \times 2} = 2^6$$
4. **Rewrite the original expression using powers of 2:**
$$4^2 \times 2^3 \times 8^2 = 2^4 \times 2^3 \times 2^6$$
5. **Use the rule of exponents for multiplication with the same base:**
$$a^m \times a^n = a^{m+n}$$
6. **Add the exponents:**
$$2^4 \times 2^3 \times 2^6 = 2^{4+3+6} = 2^{13}$$
7. **Calculate the final value:**
$$2^{13} = 8192$$
**Final answer:** $$4^2 \times 2^3 \times 8^2 = 8192$$