Fractions and Exponents.

[carllecat]

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

A) 17
B) 18
C) 34
D) 35
E) 36

Answer to be posted later.

[carllecat]

D) 35

[carllecat]

Anyone???

[Ian Stewart]

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

A) 17
B) 18
C) 34
D) 35
E) 36

Answer to be posted later.

You can prime factorize, and use exponent rules:

* The left side of the equation is equal to (1/5^m)*(1/(2^2)^18) = 1/[5^m * 2^36]
* The right side of the equation is equal to 1/[(2)*(2*5)^35] = 1/[ (2^1) * (2^35 * 5^35) ] = 1/[ 2^36 * 5^35]

The left and right sides are equal, so we have:

1/[5^m * 2^36] = 1/[ 2^36 * 5^35]

Now cross multiply, or take reciprocals on both sides, and cancel the 2^36 to find:

5^m = 5^35
m = 35

[carllecat]

Thanks Ian, easy to understand.

Cheers.