1. The problem is to understand and work with indices (exponents) in algebra. 2. The basic rule of indices is that for any base $a$ and integers $m$ and $n$: - $a^m \times a^n = a^{m+n}$ (product rule) - $\frac{a^m}{a^n} = a^{m-n}$ (quotient rule) - $(a^m)^n = a^{mn}$ (power of a power) - $a^0 = 1$ (zero exponent rule, if $a \neq 0$) - $a^{-n} = \frac{1}{a^n}$ (negative exponent rule) 3. For example, simplify $2^3 \times 2^4$: $$2^3 \times 2^4 = 2^{3+4} = 2^7 = 128$$ 4. Another example, simplify $\frac{5^6}{5^2}$: $$\frac{5^6}{5^2} = 5^{6-2} = 5^4 = 625$$ 5. To simplify $(3^2)^4$: $$ (3^2)^4 = 3^{2 \times 4} = 3^8 = 6561$$ 6. Remember, indices tell us how many times to multiply the base by itself. This explanation covers the fundamental rules and examples of indices.