Question

Which of the following has the greatest value?

• A. $(6^2\times 6{)}^4$
• B. $(36{)}^5$
• C. $({36}^2\times 6^3{)}^2$
• D. $(216{)}^4$
• E. $(6^4{)}^4$

Answer 1

The correct option is E $(6^4{)}^4$

1. ${(6^2\times 6)}^4={{(6}^3)}^4=6^{12}$
   
2. ${36}^5={\left(6^2\right)}^5=6^{10}$
3. ${({36}^2\times 6^3)}^2={(6^4\times 6^3)}^2={\left(6^7\right)}^2=6^{14}$
4. ${216}^4={\left(6^3\right)}^4=6^{12}$
5. ${\left(6^4\right)}^4=6^{16}$

• Therefore option $E$ has maximum value