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GMAT Prep Practice Test Quant Questions

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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GMAT Prep Practice Test Quant Questions

by simpm14 » Mon Apr 01, 2019 3:30 pm
I just took my first free official GMAC Practice Test and since they do not provide explanations am trying to figure out the ones I got wrong.

What does M=? The answer is 35 and I don't understand why.

Thanks for all of your help. $$\frac{1}{5}^{^M}\cdot\frac{1}{4}^{^{18}}\ =\ \frac{1}{\left(2\right)\left(10\right)^{35}}$$

*Note* The ^M and the ^18 apply to the entire fraction, the ^35 only applies to the 10.
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by ceilidh.erickson » Thu Apr 04, 2019 10:11 am
Since negative exponents indicate the reciprocal of base to the positive exponent, we can rewrite our exponents and bases:

$$\left(\frac{1}{5}\right)^M=5^{-M}$$
$$\left(\frac{1}{4}\right)^{18}=4^{-18}=2^{-36}$$
$$\frac{1}{\left(2\right)\left(10\right)^{35}}=(2^{-1})(10^{-35})=(2^{-1})((5\cdot2)^{-35})=(2^{-36})(5^{-35})$$

Thus:
$$5^{-M}\cdot2^{-36}=(2^{-36})(5^{-35})$$
$$5^{-M}=5^{-35}$$
-M = -35
M = 35

Hope this helps!
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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