math POWER

[francoisph]

Hi,

could you resolve below?

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

thks

[papgust]

I searched the forum with keyword "(1/5)^m". And i got so many links. To name a few,

https://www.beatthegmat.com/1-5-m-1-4-10 ... 56166.html
https://www.beatthegmat.com/gmatprep-exp ... t8855.html

Please do search for a question next time before you post. Thank you!

[Rich@VeritasPrep]

Hi there,

Just to clarify what you're posting, I'm taking what you wrote to mean the following:

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

If that's the case, then here's the approach:

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

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

At this point, you can actually stop, because you'll notice that on the right side of the equation, 5^35 is the only term involving a base of 5. The left side of the equation has only one term involving base 5, so we can conclude that the two base 5 terms must have the same exponent.

Final answer: [spoiler]m = 35[/spoiler]

[francoisph]

THKS ZAZ YOUR METHOD IS QUICK AND FAST

NO NEED OF ANY CALCULATION

THKS