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Exercise 1

1. Calculate:

• $A = 3^2 + 4^2$
• $B = \left(\frac{4}{5} - 5^{-1}\right)^2$

2. Write the following expressions as a power:

• $C = \left[(-3)^5\right]^2 \times \left(\frac{1}{2}\right)^8$
• $D = x^{-1} \times (x^2)^{-3}$

Exercise 2

1. Calculate and simplify:

• $A = \sqrt{6^2 + 8^2}$
• $B = 5\sqrt{3} - 4\sqrt{27} + 10\sqrt{48}$
• $C = \sqrt{2} \times \sqrt{6} \times \sqrt{3}$
• $D = (3\sqrt{5} - 2)(3\sqrt{5} + 2)$

2. Calculate:

• $C = (\sqrt{5} - 1)^2$
• $D = (3\sqrt{5} - 2)(3\sqrt{5} + 2)$

3. Rationalize the following denominators:

• $E = \frac{-3}{\sqrt{5}}$
• $F = \frac{\sqrt{2} + 3}{\sqrt{2} - 1}$
• $G = \frac{\sqrt{3}}{\sqrt{2} + \sqrt{5}}$

4. Write in scientific notation:

• $K = 20000000 \times 10^{-3}$
• $L = 0.0073 \times 10^3$

Would you like me to solve all these problems step-by-step, or do you have specific ones in mind? Let me know!

Questions for you:

1. Should I focus on any specific part of this exercise?
2. Would you like detailed explanations for simplifications?
3. Do you need help understanding powers or scientific notation?
4. Should I verify solutions with alternative methods if possible?
5. Do you want explanations about rationalizing denominators?

Tip: When working with powers, remember that $(a^m)^n = a^{m \cdot n}$.