Question

Arrange the following in descending order: (A) $3^{3^3}$ (B) $3^{(33)^3}$ (C) $(3^3)^{33}$ (D) $3^{333}$ Choose the correct answer from the options given below:

Accepted Answer

A. Let's examine the powers of 3: - (A) $3^{3^3} = 3^{27}$ - (B) $3^{(33)^3} = 3^{35937}$ - (C) $(3^3)^{33} = 3^{99}$ - (D) $3^{333}$ Comparing exponents of $3$: In (A), $3^3 = 27$, so $3^{3^3} = 3^{27}$ in exponent notation. If evaluated as a tower of powers $3^{(3^3)} = 3^{27}$, the exponents are $27, 33^3, 99, 333$. Comparing the values gives $A > B > D > C$.

Descending Order of Exponents

Explanation

Practise this under exam conditions