An algebra problem by fred fan

Algebra Level 1

Which of the following numbers is larger?

3 216 2 3 72 3^{216} \qquad \qquad 23^{72}

2 3 72 23^{72} 3 216 3^{216}

Fred Fan by fred fan , 21, Canada

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2 solutions

Joe Mansley
Jul 30, 2016

3^216 = (3^3)^72 = 27^72 > 23^72

6 Helpful 0 Interesting 0 Brilliant 0 Confused
Hung Woei Neoh
Aug 3, 2016

3 216 = 3 3 × 72 = ( 3 3 ) 72 = 2 7 72 3^{216} = 3^{3\times 72} = (3^3)^{72}=27^{72}

Since both exponents are the same, we can compare these two numbers.

27 > 23 2 7 72 > 2 3 72 3 216 > 2 3 72 27>23\\ 27^{72}>23^{72}\\ 3^{216}>23^{72}

Therefore, the larger number is 3 216 \boxed{3^{216}}

3 Helpful 1 Interesting 0 Brilliant 0 Confused

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