https://file.aiquickdraw.com/mathbot/file/1729770103887zdos42dt.jpg

Let's solve the expressions given in the image:

### a. \( 8a^4b^3 \times 6a^2b^4 \)

- First, multiply the coefficients: \( 8 \times 6 = 48 \).
- For the variables, apply the product rule of exponents: \( a^4 \times a^2 = a^{4+2} = a^6 \) and \( b^3 \times b^4 = b^{3+4} = b^7 \).

So, the solution is:
\[
48a^6b^7
\]

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### d. \( a^{3x} \times a^{4x} \)

- Apply the product rule of exponents again: \( a^{3x} \times a^{4x} = a^{(3x + 4x)} = a^{7x} \).

So, the solution is:
\[
a^{7x}
\]

---

### g. \( \frac{x^5y^9}{x^3y^4} \)

- Use the quotient rule of exponents: \( \frac{x^5}{x^3} = x^{5-3} = x^2 \) and \( \frac{y^9}{y^4} = y^{9-4} = y^5 \).

So, the solution is:
\[
x^2y^5
\]

---

Would you like more details or have any questions? Here are some related questions for further practice:

1. How do you simplify \( (2a^3b^2)^2 \)?
2. What is \( a^{2x} \times a^{5x} \times a^x \)?
3. Simplify \( \frac{x^7y^8}{x^2y^5} \).
4. What is the result of \( 10a^5b^3 \times 3a^2b^4 \)?
5. Solve \( \frac{a^{4m}}{a^m} \).

**Tip:** Always remember that when multiplying terms with the same base, you add the exponents, and when dividing, you subtract the exponents!

The image contains three algebraic expressions to simplify: 8a^4b^3 × 6a^2b^4, a^3x × a^4x, and x^5y^9 ÷ x^3y^4.

Learn how to simplify algebraic expressions such as 8a^4b^3 × 6a^2b^4, a^3x × a^4x, and x^5y^9 ÷ x^3y^4. This problem focuses on exponent rules and is suitable for students in Grades 8-10.

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