Like terms and algebraic index rules

(a) $5m + 8n$

• M1 Establishing $7m-2m+3n+5n$ or an equivalent valid method.
• A1 Correct answer: $5m + 8n$

(a) $2x^{3}y^{2}$

• M1 Divide the coefficients and subtract powers of each matching base.
• A1 Correct answer: $2x^{3}y^{2}$

(b) $-144$

• M1 Keep brackets around the negative base raised to an odd power.
• A1 Correct answer: $-144$

(a) $\frac{27x^6y^3}{9xy^2} = 3x^5y$

• M1 Expanding the numerator to $27x^6y^3$.
• A1 Dividing correctly to reach $3x^5y$ with each index shown.

(b) $y = 3$

• P1 Writing $4^y$ as $2^{2y}$.
• P1 Forming the equation $x + 2y = 10$.
• P1 Solving with $x + y = 7$ (subtracting or substituting).
• A1 The correct answer, $y = 3$.