fractions and exponents

[deagez]

This one is from the mba.com practice test

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

m=?

answer is 35, why? no idea. HELP!

[life is a test]

This one is from the mba.com practice test

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

m=?

answer is 35, why? no idea. HELP!

I believe the rhs is supposed to read 1/ (2(10^35)) in which case:
(1/5^m )(1/2^(2^18)) = (1/(2*(2^35)(5^35)) -> (1/5^m )(1/2^36) = (1/((2*36)(5^35))-> comparing lhs to rhs gives you m = 35.

[deagez]

thank you for explanation, however, I do not understand the following:

[(1/5)^35][(1/2)^36]=1/(5^35)(2^36)

please explain how the fractions with exponents are able to be combined like they are in the final step of this problem.

[life is a test]

thank you for explanation, however, I do not understand the following:

[(1/5)^35][(1/2)^36]=1/(5^35)(2^36)

please explain how the fractions with exponents are able to be combined like they are in the final step of this problem.

LHS must = RHS
1/2)^36 is same on either side so they cancel out but for (1/5)^m to cancel out with (1/5)^35 m must be 35.

Note that you can only subsitute the left hand side exponents with the right hand side exponents like this because the base is equal. If the base was different, you would have to reduce it to make it equal or else you couldn't use this method to solve.

Hope that helps