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We are GMAT Mentors, a non-profit focused on facilitating the free exchange of GMAT knowledge, support, and advice through one-on-one mentoring.
Since launching our service, we have gotten a lot of positive feedback from both mentees and mentors! We have had requests to start a tip/principle of the week, so we have decided to do just that. Each week we post a tip, trick, or principle focusing in either Verbal or Quant. You may already know some of these, but hopefully you will see something new!
This weeks tip focuses on the quick way to solve large exponent equations. Ultimately, it all comes down to prime factors and cancelling out like prime factors. This is best shown through example:
Question: If (⅕)^m*(¼)^18= 1/(2*10^35), then m=
Answer choices: 17, 18, 34, 35, 36
In order to solve this, you should automatically think “base prime numbers”. In doing that, you breakdown all numbers to their simplest prime factor form. It is also helpful to make all denominators in the numerator:
5^(-m)*2^(-18)*2^(-18)=2^(-1)*5^(-35)*2^(-35)
Now it is easier to cancel out similar prime factors, which in this case cancels out all of the 2s in the equation, since 2^(-36) is on each side.
The result is 5^(-m)=5^(-35) so m=35. This is a good example of how to break down any equation with large exponents. The GMAT will never make you calculate a large exponent. Whenever you see a large exponent, always think 1) break down to prime factors and 2) cancel out similar prime factors to reduce the exponent.
Thanks for reading and as always - If you would like to become a mentee and receive personalized support or become a mentor and help others, please check out our website or email us!
Email: [email protected]
Website: https://www.gmatmentors.com
Since launching our service, we have gotten a lot of positive feedback from both mentees and mentors! We have had requests to start a tip/principle of the week, so we have decided to do just that. Each week we post a tip, trick, or principle focusing in either Verbal or Quant. You may already know some of these, but hopefully you will see something new!
This weeks tip focuses on the quick way to solve large exponent equations. Ultimately, it all comes down to prime factors and cancelling out like prime factors. This is best shown through example:
Question: If (⅕)^m*(¼)^18= 1/(2*10^35), then m=
Answer choices: 17, 18, 34, 35, 36
In order to solve this, you should automatically think “base prime numbers”. In doing that, you breakdown all numbers to their simplest prime factor form. It is also helpful to make all denominators in the numerator:
5^(-m)*2^(-18)*2^(-18)=2^(-1)*5^(-35)*2^(-35)
Now it is easier to cancel out similar prime factors, which in this case cancels out all of the 2s in the equation, since 2^(-36) is on each side.
The result is 5^(-m)=5^(-35) so m=35. This is a good example of how to break down any equation with large exponents. The GMAT will never make you calculate a large exponent. Whenever you see a large exponent, always think 1) break down to prime factors and 2) cancel out similar prime factors to reduce the exponent.
Thanks for reading and as always - If you would like to become a mentee and receive personalized support or become a mentor and help others, please check out our website or email us!
Email: [email protected]
Website: https://www.gmatmentors.com
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