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.