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

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(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