Question

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

Answer 1

flipping all the fractions gives :
\[5^{m} 4^{18} = 2(10)^{35}\]
10 is 5 times 2, so now we have:
\[5^{m} 4^{18} = (2) 5^{35} 2^{35} \Longrightarrow 5^{35}2^{36} \]
But 4 is 2 squared, so the right side changes:
\[5^{m} 4^{18} = 5^{35} 4^{18}\]
so m = 35

Answer 2

Thank you. Can you explain why you are able to flip the fractions?

Answer 3

As a result of the fact that there is no addition/subtraction going on in the problem (only multiplication and division), we can combine the fractions on the left hand side of the problem into on weird looking fraction. its going to be in the form of:\[\frac{1} {stuff} = \frac{1}{something else} \]
then you can either cross multiply, or just flip both sides, which ever you prefer :)