1. The problem is to solve expressions involving indices (powers or exponents). 2. Indices follow rules such as multiplying same bases by adding powers: $a^m \times a^n = a^{m+n}$, and powers raised to powers by multiplying: $(a^m)^n = a^{mn}$. 3. Example: Simplify $2^3 \times 2^4$. Using the rule, $2^{3+4} = 2^7 = 128$. 4. Another example: Simplify $(3^2)^4$. Multiply powers: $3^{2 \times 4} = 3^8 = 6561$. 5. For division: $a^m \div a^n = a^{m-n}$. Example: $5^6 \div 5^2 = 5^{6-2} = 5^4 = 625$. 6. To raise a product to a power: $(ab)^n = a^n b^n$. Example: $(2 \times 3)^3 = 2^3 \times 3^3 = 8 \times 27 = 216$. 7. To raise a quotient to a power: $(\frac{a}{b})^n = \frac{a^n}{b^n}$. Example: $(\frac{4}{2})^2 = \frac{4^2}{2^2} = \frac{16}{4} = 4$. 8. Negative indices indicate reciprocal: $a^{-n} = \frac{1}{a^n}$. Example: $2^{-3} = \frac{1}{2^3} = \frac{1}{8}$. 9. Zero power: $a^0 = 1$ for any $a \neq 0$. Example: $7^0 = 1$. 10. These are the fundamental rules to solve problems with indices effectively.