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: $48a^6b^7$

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!