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# Exponents Problem solution

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Exponents Problem solution [#permalink]  11 Mar 2007, 15:21
Can anyone help me solve this problem?

(1/5)^m * (1/4)^18 = (1/(2*10^35)). What is the value of m?
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(1/5)^m*(1/4)^18 = 1/(2*10^35)

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

(1/5^m)*(1/2^36) = 1/(2*10^35) 4^18 = (2^2)^18 = 2^36

1/((5^m)*(2^36)) = 1/(2*10^35)

since we need 35 of 10s, and 2*5=10, we'll need 35 of 5s to go with 35 of 2s. and the remaining one 2 can go in front.

Therefore, m=35.

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

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

(1/5^m)*(1/2^36) = 1/(2*10^35) 4^18 = (2^2)^18 = 2^36

1/((5^m)*(2^36)) = 1/(2*10^35)

since we need 35 of 10s, and 2*5=10, we'll need 35 of 5s to go with 35 of 2s. and the remaining one 2 can go in front.

Therefore, m=35.

Good explanation.

From the highlighted equation...
1/((5^m)*(2^36)) = 1/(2*10^35)
=> 1/((5^m)*(2^36)) = 1/(2*2^35*5^35)
=> 1/((5^m)*(2^36)) = 1/(5^35*2^36)

So, 5^m*2^36 = 5^35*2^36
Therefore, m=35
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