Question
Download Solution PDFWhat should come in place of the question mark (?) in the following question?
\((2 \times 3)^3 \times (4 \times 9)^2 \times (27 \times 8)^2 = (6)^? \)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
(2 × 3)3 × (4 × 9)2 × (27 × 8)2 = (6)?
Formula used:
For simplification: (a × b)n = an × bn
Calculation:
(2 × 3)3 × (4 × 9)2 × (27 × 8)2 = (6)?
⇒ (23 × 33) × (42 × 92) × (272 × 82) = (6)?
⇒ (8 × 27) × (16 × 81) × (729 × 64) = (6)?
⇒ Combine powers of 2 and 3:
⇒ 23 × 24 × 26 × 33 × 34 × 36 = (6)?
⇒ 2(3+4+6) × 3(3+4+6) = (6)?
⇒ 213 × 313 = (6)?
⇒ (2 × 3)13 = (6)?
⇒ 613 = 6?
⇒ ? = 13
∴ The correct answer is option (1).
Last updated on Mar 12, 2025
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