exponents problem

[LFalken]

What is the Value of 'm' ?

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


I believe m=35

could someone please find the time to verify this is the correct answer and explain the solution. I would be very thankful if so... I'm having trouble with this one....

[ssmiles08]

IMO 35 as well.

1/(2*10^35) = 1/(2*(2*5)^35)

5^35 = 5^m

[LFalken]

Ssmiles08,

Thank you very much! But could you elaborate some on the solution... I'm not seeing what you did with the (1/4)^18 value that (1/5)^m is multiplied by... showing a few steps would be great. Thanks!

[LFalken]

Ssmiles08,

Thank you very much! But could you elaborate some on the solution... I'm not seeing what you did with the (1/4)^18 value that (1/5)^m is multiplied by... showing a few steps would be great. Thanks!

[ssmiles08]

Ssmiles08,

Thank you very much! But could you elaborate some on the solution... I'm not seeing what you did with the (1/4)^18 value that (1/5)^m is multiplied by... showing a few steps would be great. Thanks!

yes sure.

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

(1/5)^m = 1/5^m

(1/4)^18 = ((1/2)^2)^18 = 1/2^36

1/((2*(10)^35)) = 1/(2*(2*5)^35)

so its 1/5^m * 1/2^36 = 1/(2*2^35*5^35)

2*2^35 = 2^36

5^35 = 5^m

[tohellandback]

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

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

(1/5)^m * (1/4)^18 = 1/(((5)^35*(2)^36))
(1/5)^m * (1/4)^18 = (1/5)^35 * (1/4)^18

so m=35

[LFalken]

ssmiles08, and tohellandback....

Thank you both very much for your responses... they both cleared things up for me. I appreciate it!