Evaluate (2 + 3) × (7 − 4)² = ?

Correct — A.
Rule: brackets first, then the power, then multiply.

First bracket: 2 + 3 = 5
Second bracket: 7 − 4 = 3
Power: 3² = 9
Multiply: 5 × 9 = 45 → option (a).

Why the others are wrong

• (b)
  75 — 75 is (2 + 3)² × (7 − 4) = 25 × 3: it squares the wrong bracket. The ² sits on (7 − 4) alone, so the product is 5 × 9.
• (c)
  40 — 40 is 5 × 8, which needs (7 − 4)² to equal 8. It equals 3² = 9, so the value is 45.
• (d)
  30 — 30 is 5 × 6: it doubles the 3 instead of squaring it. The index ² means 3 × 3 = 9, not 3 × 2.

The order of operations fixes the route: work inside each bracket, then apply powers, then multiply or divide, then add or subtract.

A power belongs only to the bracket it is written on. Here ² sits on (7 − 4), so only that bracket is squared.

A quick check: the answer must be 5 times a perfect square, and 45 = 5 × 9 is the option of that form.

Key facts

• Work inside a bracket before applying a power to it.
• (7 − 4)² = 3² = 9, whereas 7² − 4² = 49 − 16 = 33.
• (2 + 3) × (7 − 4)² = 5 × 9 = 45.

Common traps

• Squaring the first bracket instead of the one the index sits on, which gives 75.
• Reading ² as × 2, which gives 30.

No directly related past PYQ was found.