Solve the following exercise:
3729=
To solve this problem, we need to evaluate 3729.
Step 1: Convert the expression into exponent form. We know 729=72921. Thus, 3729=(72921)31.
Step 2: Apply the formula for exponents (am)n=am⋅n. Thus, (72921)31=7292⋅1/31=72961.
Step 3: Find the base of 729 as a power of an integer. Observing, 729 = 36 because 36=729.
Step 4: Substitute the power of the base: 72961=(36)61=36⋅61=31=3.
Therefore, the solution to the problem is 3729=3.