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Comparing values with exponent

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by GMATGuruNY » Tue May 29, 2012 9:29 am
serenayc wrote:Which value is bigger: 4^(7/8) or 5^(4/5)?

I am interested in learning the approach to compare values with exponent of different bases. Can someone please explain? Thanks a lot!
4^(7/8) > 5^(4/5)?

To clear the fractions, raise each side to the 40th power:
(4^(7/8))�� > (5^(4/5))��
4³� > 5³²

Compare POWERS OF 10 by multiplying each side by 2³² and recognizing that 2¹� = 1024 ≈ 10³:
2³² * 4³� > 2³² * 5³²
2³² * 2�� > (2*5)³²
2¹�² > 10³²
(2¹�)¹� * 2² > 10³²
(10³)¹� * 2² > 10³²
10³� * 2² > 10³²

The righthand side is much greater than the lefthand side.
Thus, 5^(4/5) > 4^(7/8).
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