1. **State the problem:** Perform the indicated operations using the theorems involving exponents. 2. **Recall the key exponent theorems:** - Product of powers: $$a^m \times a^n = a^{m+n}$$ - Quotient of powers: $$\frac{a^m}{a^n} = a^{m-n}$$ - Power of a power: $$(a^m)^n = a^{m \times n}$$ - Power of a product: $$(ab)^m = a^m b^m$$ - Power of a quotient: $$\left(\frac{a}{b}\right)^m = \frac{a^m}{b^m}$$ 3. **Apply these rules step-by-step to the given expression (example):** Suppose the expression is $$\frac{2^3 \times 2^4}{2^5}$$ 4. **Simplify numerator using product of powers:** $$2^3 \times 2^4 = 2^{3+4} = 2^7$$ 5. **Rewrite the expression:** $$\frac{2^7}{2^5}$$ 6. **Simplify using quotient of powers:** $$2^{7-5} = 2^2$$ 7. **Final answer:** $$2^2 = 4$$ This method applies to any similar problem involving exponents by carefully using the exponent theorems step-by-step.