Question

Which is the greatest among $(3)^{198},(27)^{64},(9)^{100}$ and $(81)^{49}$ ?

• A. $(9)^{100}$
• B. $(81)^{49}$
• C. $(27)^{64}$
• D. $(3)^{198}$

Answer 1

Answer: (A)

$3^{198},(27)^{64},(9)^{100},(81)^{49}$
Converting all the numbers with base 3 . $27^{64}=(3^3)^{64}=3^{192}$
$(9)^{100}=(3^2)^{100}=3^{200}$
$(81)^{49}=(3^4)^{49}=3^{196}$
$3^{200}$ is the greatest.
$\therefore 9^{100}$ is the greatest.