Question

Which of the following expressions has the largest value?

• A. ${\left(3^4\right)}^{13}$
• B. ${\left[{\left(3^{30}\right)}^{12}\right]}^{\frac{1}{10}}$
• C. $3^{30}+3^{30}+3^{30}$
• D. ${\left(3^{100}\right)}^{\frac{1}{2}}$

Answer 1

The correct option is A ${\left(3^4\right)}^{13}$

Use the rules of exponents to simplify each expression:
(A) ${\left(3^4\right)}^{13}=3^{52}$
(B) ${\left[{\left(3^{30}\right)}^{12}\right]}^{\frac{1}{10}}={\left(3^{360}\right)}^{\frac{1}{10}}=3^{\frac{360}{10}}=3^{36}$
(C) $3^{30}+3^{30}+3^{30}=3\left(3^{30}\right)=3^{31}$
(D) ${\left(3^{100}\right)}^{\frac{1}{2}}={\left(3^{}\right)}^{\frac{100}{2}}=3^{50}$
Answer choice (A) is clearly larger than (B), (C) and (D).