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GMATPrep, m = ?, Searched but didn't see
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fueledGMAT
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I will admit that exponents are an area I need serious work on, but can someone please help?
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
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Quick Review:
(a * b) ^ c = a^c + b^c
So:
1/(2 * 10^35)
= 1 / (2 * (2*5)^35)
= 1 / (2 * 2^35 * 5^35)
= 1 / (2^36 * 5^35)
= 1 / (4^18 * 5^35) // Note that 2*2 = 4, so 2^36 = 4^18
= (1 / 4^18) * (1/5^35) // Note that 1 = 1^18 = 1^35
= (1/4)^18 * (1/5)^35
= (1/4)^18 * (1/5)^m
so m = 35
(a * b) ^ c = a^c + b^c
So:
1/(2 * 10^35)
= 1 / (2 * (2*5)^35)
= 1 / (2 * 2^35 * 5^35)
= 1 / (2^36 * 5^35)
= 1 / (4^18 * 5^35) // Note that 2*2 = 4, so 2^36 = 4^18
= (1 / 4^18) * (1/5^35) // Note that 1 = 1^18 = 1^35
= (1/4)^18 * (1/5)^35
= (1/4)^18 * (1/5)^m
so m = 35
Last edited by chetane on Mon Nov 21, 2011 12:36 am, edited 1 time in total.
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ikaplan
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One quick hint: whenever you see 10 raised on certain exponent, see the other numbers involved in the equation and try to realize whether you will need to break up the 10 into 2s and 5s (2*5).
In this case, on the left side you have 5 and 4 and on the right- 10. This tells you that you should rewrite the equation by using the exponent rules in a way that breaks up existing numbers into 2s and 5s. To be more precise, the initial equation can be re-written as follows: 5^-m*2^-36=2^-1*2^-35*5^-35
In this case, on the left side you have 5 and 4 and on the right- 10. This tells you that you should rewrite the equation by using the exponent rules in a way that breaks up existing numbers into 2s and 5s. To be more precise, the initial equation can be re-written as follows: 5^-m*2^-36=2^-1*2^-35*5^-35
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vishal chugh
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since on left side,,,you have 1/5 with power of 35.. other nos. does not mean. here both sides will be equal when both sides have 1/5 raised to power 35; so this can be done without solving as 10 = 2*5
