GMAT Prep - Exponents

Question

Could someone please explain me solution for this question? I ofcourse got it wrong.

gmatnub · Answer

Just ignore the numerator

5^m * 4^18 = 5^m * 2^36

2(10^35) = 2^1 * 2^35 * 5^35

m = 35

albertrahul · Answer

Thanks for the explanation!
However, I could not understand following line:

2(10^35) = 2^1 * 2^35 * 5^35

Please elaborate.

gmatnub · Answer

2 is 2^1

(10^35) is 2^35 * 5^35 ---> if the exponents are the same, you can multiple the bases.

brokerbevo · Answer

IF (1/5)^m * (1/4)^18 = 1/(2(10)^35)

since 1 to any power is 1, we treat 1^m as just 1 so therefore:
1/(5^m) * 1/(4^18) = 1/(2*(10^35))

Since all these parts are written as a fraction with 1 as the numerator, we can just write out the denominators without the numerator:
(5^m) * (4^18) = 2*(10^35)

The 4^18 figure can be re-written as (2^2)^18 or 2^36 AND the 10^35 figure can be re-written as 2^35 * 5^35:
(5^m) * (2^36) = 2*(2^35)*(5^35)

Then combine the 2's on the right side (then cancel out the 2's from the left side):
(5^m) * (2^36) = (2^36)*(5^35) --> (5^m) = (5^35)

From this, we can see that m = 35

albertrahul · Answer

Thank You Both!
It makes sense now.

GMAT Prep - Exponents

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