SOLUTION: Without using a calculator which is larger: x= 7^1/4 or y=4^1/3

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Question 992257: Without using a calculator which is larger: x= 7^1/4 or y=4^1/3
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Which is larger? (without using a calculator)

matrix%282%2C1%2C%22%22%2C7%5E%281%2F4%29%29%22%3F%22matrix%282%2C1%2C%22%22%2C4%5E%281%2F3%29%29

Rewrite the exponents with a common denominator

matrix%282%2C1%2C%22%22%2C7%5E%283%2F12%29%29%22%3F%22matrix%282%2C1%2C%22%22%2C4%5E%284%2F12%29%29

Get them with a common fraction exponent:

matrix%282%2C1%2C%22%22%2C%287%5E3%29%5E%281%2F12%29%29%22%3F%22matrix%282%2C1%2C%22%22%2C%284%5E4%29%5E%281%2F12%29%29

Evaluate the bases without a calculator:

7%5E3=7%2A7%2A7=49%2A7=343, 4%5E4=4%2A4%2A4%2A4=16%2A16=256 

matrix%282%2C1%2C%22%22%2C343%5E%281%2F12%29%29%22%3F%22matrix%282%2C1%2C%22%22%2C256%5E%281%2F12%29%29

And since 343 > 256

matrix%282%2C1%2C%22%22%2C343%5E%281%2F12%29%29%29%22%22%3E%22%22matrix%282%2C1%2C%22%22%2C256%5E%281%2F12%29%29%29

So

matrix%282%2C1%2C%22%22%2C7%5E%281%2F4%29%29%22%22%3E%22%22matrix%282%2C1%2C%22%22%2C4%5E%281%2F3%29%29


Edwin