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how to compare numbers without a
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calculator the problem is this which is
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greater 17 raised to the power of 97 or
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63 raised to the power of
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64 as usual pause the video before
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watching and try to solve this problem
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on your own it is convenient to compare
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Powers when either their bases are equal
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or their exponents are equal in this
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case neither of those conditions is met
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but we can notice that the bases of the
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powers are close to powers of two 17 is
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close close to 16 and 63 is close to 64
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for those who might have forgotten 16 is
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2 raised to the power of 4 and 64 is 2
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ra to the power of 6 we will try to use
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this to our advantage let's take the
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first number 17 ra to the power of 97
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this is greater than 16 raised to the
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power of 97 we can replace 16 with 2
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raised to the power of 4 when raising a
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power to another Power the exponents are
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multiplied so we get 2 raised to the
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power of 4 * 97 or 2 2 ra to the power
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of 388 thus 17 ra to the^ of 97 is
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greater than 2 ra to the power of 388
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now let's take the second number 63 raed
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to the power of 64 this is less than 64
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raed to the power of 64 64 is 2 raed to
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the power of 6 again when raising a
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power to another Power the exponents are
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multiplied so we get 2 raised to the
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power of 6 * 64 or 2 ra to the^ of 384
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thus the second number is less than 2 ra
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raised to the power of 384 now we can
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compare the two the first number 17
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raised to the power of 97 is greater
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than 2 raised to the power of 388 and
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that is greater than 2 raised to the
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power of 384 which is greater than the
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second number 63 ra to the power of 64
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so the first number is greater than the
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second the final answer is that 17 ra to
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the power of 97 is greater the problem
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is solved if you understood the solution
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please like the video leave a comment
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