Exponents and Fractions

[masuarezdl]

Any clues on this one?

If (1/5)^m * (1/4)^18 = 1/2(10)^35, then m=
a) 17
b) 18
c) 34
d) 35
e) 36

[tohellandback]

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

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

[ketkoag]

same approach as above..
35 it is..

[uw490]

I'm a little rusty on my rules for exponents...

But, how can you turn (1/4)^18 into (1/2)^36 and how can you turn (10)^35 into (1/2)^35*(1/5)^35???

An explanation of the above would really help me out.

thanks
J

[mike22629]

First think of it this way:

What does (1/2)^36 actually equal?

It equals:
(1^36)/(2^36)

Now what does 4^2 = ?
It equals 16 or 2*2*2*2 or 4*4

So.....
2^36 = 4^18
(There are the same number of 2s on both sides of equation, they are just written differently. Remember that 4 = 2*2, so 4 is essentially two 2s.

Just as 4^2 = 2^4

And you do not turn 10^35 into (1/2^35)*(1/5^35)

You turn 1/(10^35) into (1/2^35)*(1/5^35)

[uw490]

Got it!

Thanks for the explanation, this clears it up!