Question

The latest value among $8^{28},{512}^9,{\left(\sqrt{2}\right)}^{282},4^{42},{32}^{16}is$

• A. $8^{28}$
• B. ${512}^9$
• C. ${\left(\sqrt{2}\right)}^{282}$
• D. None of these

Answer 1

Answer: (C)

${\left(\sqrt{2}\right)}^{282}$

The largest value among

$8^{28}={\left[{\left(2\right)}^3\right]}^{28}=2^{84}$

${512}^9={\left[{\left(2\right)}^9\right]}^9=2^{81}$

${\left(\sqrt{2}\right)}^{282}={\left[{\left(2\right)}^{\frac{1}{2}}\right]}^{282}=2^{141}$

$4^{42}={\left[{\left(2\right)}^2\right]}^{42}=2^{84}$

${32}^{16}={\left[{\left(2\right)}^5\right]}^{16}=2^{80}$

Hence, ${\left(\sqrt{2}\right)}^{282}={\left[{\left(2\right)}^{\frac{1}{2}}\right]}^{282}=2^{141}$ is largest number.