math question (anyone know how to solve)

[LSJK]

math question (anyone know how to solve):

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

what does m=?

Answer options:

17, 18, 34, 35, 36

[vasbli]

(1/5)^m * (1/4)^18 = 1/2(10)^35
--------
(1/5)^m * (1/4)^18=(1/5)^m * (1/2)^36=(1/5)^m * 1/(2*2^35)
and
1/2(10)^35=1/(2*5^35*2^35)

m=35

[LSJK]

thank you.

[BlindVision]

(1/5)^m * (1/4)^18 = 1/2(10)^35
--------
(1/5)^m * (1/4)^18=(1/5)^m * (1/2)^36=(1/5)^m * 1/(2*2^35)
and
1/2(10)^35=1/(2*5^35*2^35)

m=35

Can you please tell me how...
(1/4)^18 became (1/2)^36?

And...

How 1/2(10)^35=1/(2*5^35*2^35) ? Thank you!

[ssmiles08]

(1/5)^m * (1/4)^18 = 1/2(10)^35
--------
(1/5)^m * (1/4)^18=(1/5)^m * (1/2)^36=(1/5)^m * 1/(2*2^35)
and
1/2(10)^35=1/(2*5^35*2^35)

m=35

Can you please tell me how...
(1/4)^18 became (1/2)^36?

And...

How 1/2(10)^35=1/(2*5^35*2^35) ? Thank you!

BlindVision,

1/4 = (1/2)^2
so [(1/2)^2]^18 = (1/2)^36


and

1/[2*10] = 1/[2*5*2] = 1/[(2*5)*(2)]
since the whole bottom of the fraction is raised to the power of 35, you need to distribute that property to all multiplied products.

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

-hope that helps.

[LSJK]

Question 1:

4= 2^2

so (2^2)^18= 2^36 because 2 * 18=36

______________________________________
Question 2:

2^2 * 2= 2^3=8

so

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

so based on above. . .

2 * 2^35 = 2^36

[BlindVision]

Aha! I get it! Thank you, SSmiles!

Thanks LSJK, I see your reply in the "post a reply" screen, but not in the regular screen.