1. The problem is to understand and solve exponential expressions, which are expressions where a number (the base) is raised to a power (the exponent). 2. The general formula for an exponential expression is $a^n$, where $a$ is the base and $n$ is the exponent. 3. Important rules for exponents include: - $a^m \times a^n = a^{m+n}$ (multiplying powers with the same base adds exponents) - $\frac{a^m}{a^n} = a^{m-n}$ (dividing powers with the same base subtracts exponents) - $(a^m)^n = a^{m \times n}$ (power of a power multiplies exponents) - $a^0 = 1$ (any nonzero number to the zero power is 1) 4. Example: Simplify $2^3 \times 2^4$. - Using the rule, $2^3 \times 2^4 = 2^{3+4} = 2^7$. - Calculate $2^7 = 128$. 5. Another example: Simplify $\frac{5^6}{5^2}$. - Using the rule, $\frac{5^6}{5^2} = 5^{6-2} = 5^4$. - Calculate $5^4 = 625$. 6. These rules help simplify and solve exponential expressions easily. Final answer: Understanding and applying exponent rules allows you to simplify expressions like $2^3 \times 2^4 = 128$ and $\frac{5^6}{5^2} = 625$.