1. **Problem statement:** Given that $2^x = 5$, find the values of: 1) $2^{x+1}$ 2) $2^{x-1}$ 3) $2^{x+2} + 2^{x+3}$ 2. **Formula and rules:** - For exponents, recall the rule $a^{m+n} = a^m \times a^n$. - Also, $a^{m-n} = \frac{a^m}{a^n}$. 3. **Step-by-step solution:** 1) Calculate $2^{x+1}$: Using the exponent addition rule: $$2^{x+1} = 2^x \times 2^1 = 5 \times 2 = 10$$ 2) Calculate $2^{x-1}$: Using the exponent subtraction rule: $$2^{x-1} = \frac{2^x}{2^1} = \frac{5}{2} = 2.5$$ 3) Calculate $2^{x+2} + 2^{x+3}$: Break down each term: $$2^{x+2} = 2^x \times 2^2 = 5 \times 4 = 20$$ $$2^{x+3} = 2^x \times 2^3 = 5 \times 8 = 40$$ Sum them: $$20 + 40 = 60$$ 4. **Final answers:** 1) $2^{x+1} = 10$ 2) $2^{x-1} = 2.5$ 3) $2^{x+2} + 2^{x+3} = 60$