Here’s the breakdown for Question 1 from the uploaded image.

These questions are based on index notation rules. Specifically:

1. When multiplying terms with the same base, add their exponents: $a^m \times a^n = a^{m+n}$

Solutions:

(a) $x^6 \times x^4$

• Add the exponents: $6 + 4 = 10$
  Answer: $x^{10}$

(d) $y \times y^6$

• Remember that $y = y^1$, so: $1 + 6 = 7$
  Answer: $y^7$

(g) $4x^5 \times 7x^3$

• Multiply the constants: $4 \times 7 = 28$
• Add the exponents for $x$: $5 + 3 = 8$
  Answer: $28x^8$

(j) $m^7 \times m^5 \times m^4$

• Add the exponents: $7 + 5 + 4 = 16$
  Answer: $m^{16}$

(l) $5xy \times 4x^2y^3 \times 3x^3y^3$

• Multiply the constants: $5 \times 4 \times 3 = 60$
• Add the exponents for $x$: $1 + 2 + 3 = 6$
• Add the exponents for $y$: $1 + 3 + 3 = 7$
  Answer: $60x^6y^7$

Would you like any of these steps further explained?

Here are 5 related questions to reinforce your learning:

1. What happens if you divide terms with the same base?
2. How would you simplify $(x^3)^4$?
3. How does the rule change if the bases are different?
4. What is the result of multiplying $0 \times x^5$?
5. Can you simplify $a^{-3} \times a^5$?

Tip: Always ensure the bases are identical before applying exponent rules!