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Q. Which is greatest among \( 3^{198}, 27^{64}, 9^{100}, 81^{49} \)?
(a) \( 9^{100} \) (b) \( 81^{49} \) (c) \( 27^{64} \) (d) \( 3^{198} \)
✏️ Solution
Convert all into base 3
\( 27^{64} = (3^3)^{64} = 3^{192} \)
\( 9^{100} = (3^2)^{100} = 3^{200} \)
\( 81^{49} = (3^4)^{49} = 3^{196} \)
Now compare: \( 3^{198}, 3^{192}, 3^{200}, 3^{196} \)
Greatest power is \( 3^{200} \)
So greatest number is \( 9^{100} \)
Correct Option: (a) \( 9^{100} \)
\( \boxed{9^{100}} \)