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GMATPrep Question - Exponents

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by VP_Tatiana » Sun Jul 20, 2008 2:01 pm
We can express the equation as:

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

(I get this because 1^m=1, and 1^18 = 1, to give me a numerator of 1, and then I multiply denominators)

Cross multiplying gives us:
(5^m)(4^18)=2*(10^35)

Since 10=5*2, I think it is best to express everything in terms of 5 and 2. Since 4=2^2, 4^18=(2^2)^18 = 2^36. This gives us:

(5^m)(2^36)=2*(10^35)

Dividing both sides by 2, I get:
(5^m)(2^35)=(10^35). Or,
(5^m)(2^35) = (2*5)^35 = (2^35)(5^35)

Dividing both sides by 2^35, we have
5^m = 5^35

Thus, m=35
Last edited by VP_Tatiana on Sun Jul 20, 2008 2:02 pm, edited 1 time in total.
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Re: GMATPrep Question - Exponents

by Ian Stewart » Sun Jul 20, 2008 2:01 pm
JDesai01 wrote:Not sure why I'm having such a hard time figuring this one out:

(1/5)^m * (1/4)^18 = 1/(2(10)^35), then m=?

Kindly help me understand how to solve. Thank you
(1/5)^m * (1/4)^18 = 1/(2(10)^35)
1/[(5^m)*(4^18)] = 1/[2*(10^35)]
1/[(5^m)*(2^2)^18] = 1/[2*(2*5)^35]
1/[(5^m)*(2*36)] = 1/[(2^36)*(5^35)]
1/5^m = 1/5^35
m = 35
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by JDesai01 » Sun Jul 20, 2008 3:24 pm
Thank you!
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If (1/5)^m * (1/4)^18 = 1/2(10_^35

by LifetimesofSC » Tue Jul 22, 2008 6:13 pm
VP_Tatiana wrote:We can express the equation as:

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

(I get this because 1^m=1, and 1^18 = 1, to give me a numerator of 1, and then I multiply denominators)

Cross multiplying gives us:
(5^m)(4^18)=2*(10^35)

Since 10=5*2, I think it is best to express everything in terms of 5 and 2. Since 4=2^2, 4^18=(2^2)^18 = 2^36. This gives us:

(5^m)(2^36)=2*(10^35)

Dividing both sides by 2, I get:
(5^m)(2^35)=(10^35). Or,
(5^m)(2^35) = (2*5)^35 = (2^35)(5^35)

Dividing both sides by 2^35, we have
5^m = 5^35

************************

(5^m)(2^36)=2*(10^35)
Dividing both sides by 2, I get:
(5^m)(2^35)=(10^35). Or,
(5^m)(2^35) = (2*5)^35 = (2^35)(5^35) ...

Can someone explain why the dividing both sides by 2 only impacted the 2^36 turning into 2^35 but not the 5^m? I'm still not clear on the 2^36 to 2^35 step.

Thanks :(

Thus, m=35
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