PIL import Image import pytesseract

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image_path = "/mnt/data/17331172185363g171h0q.jpg" extracted_text = pytesseract.image_to_string(Image.open(image_path))

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Question 2
Simplify the following:
(a) $3(x + 2) + 5(2x + 3)$
(b) $\frac{7^{-2} \cdot 3^{-2}}{3^5 \cdot 7^4 \cdot 7^{-3}}$

Let me solve each part step by step:

Part (a):

$3(x + 2) + 5(2x + 3)$

1. Distribute the terms: $3x + 6 + 10x + 15$

2. Combine like terms: $(3x + 10x) + (6 + 15) = 13x + 21$

Solution for (a): $13x + 21$

Part (b):

$\frac{7^{-2} \cdot 3^{-2}}{3^5 \cdot 7^4 \cdot 7^{-3}}$

1. Combine the powers of 7 and 3:

   • For $7$: $7^{-2 - 4 + 3} = 7^{-3}$
   • For $3$: $3^{-2 - 5} = 3^{-7}$

   The expression simplifies to: $\frac{1}{7^3 \cdot 3^7}$

2. Write as a single power: $\frac{1}{21^{10}}$

Solution for (b): $\frac{1}{7^3 \cdot 3^7}$ or $\frac{1}{21^{10}}$ if simplified further.

Let me know if you need further clarification or detailed steps! Here are 5 related questions and a tip:

Related Questions:

1. How do you handle distribution when variables are present in expressions like (a)?
2. What are the laws of exponents used to simplify powers in (b)?
3. Can you explain why $a^m \cdot a^n = a^{m+n}$ is valid?
4. How can you simplify fractions involving multiple bases and powers more efficiently?
5. What happens if a denominator has a negative exponent?

Tip:

Always simplify powers and expressions step by step to avoid errors, especially when combining bases.