GMAT Prep Practice Test Quant Questions

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!