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Question

Which is the greatest 312,215,56. What is the general approach to solve.


Solution

312 greater among all. There is no common base for the given example to have the general approach. 531441 312 = 215=32768, 56=15625
You can make use of Power rule
Step 1
Find the prime factors of the exponent.
Exampl: 312
12=2×6
12=2×2×3

Step 2
Use the power rule for exponents to set up the problem. The power rule states: (xa)b=x(a×b)
312=3(2×2×3)=(((32)2)3)

Step 3
Solve the problem from the inside out.
(((32)2)3=((92)3)=(813)=531441

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