Explanation

First recognize that 2^(-4) and 3^(-2) are both POSITIVE, whereas -20 and -10 are both NEGATIVE.
So, if we want a product that's between -1 and 0 (i.e., NEGATIVE), we need one positive value and one negative value.

Let's try some pairs:

-20 and 2^(-4)
-20 x 2^(-4) = -20 x 1/16
= -20/16
= -5/4
= -1.25
NO GOOD!

-20 and 3^(-2)
-20 x 3^(-2) = -20 x 1/9
= -20/9
= -2 2/9
NO GOOD!

-10 and 2^(-4)
-10 x 2^(-4) = -10 x 1/16
= -10/16
= -5/8
= -0.375
PERFECT!

The answer is -10 and 2^(-4)

ASIDE: Also, the product of -10, 2^(-4) and 3^(-2) works as well.
-10 x 2^(-4) x 3^(-2) = -10 x 1/16 x 1/9
= -10/144
This product is also between -1 and 0

Cheers,
Brent
_________________

Bump

Process
1. Recall that a negative exponent moves the whole term to the opposite side of the fraction bar in the final analysis: hence, 2^-4 = 1/(2^4) = 1/16.
2. 2^-4 and 3^-2 are both positive fractions.
3. -20 and -10 are both negative.
4. We only need to pick two numbers, so let's go with our safest bet and choose the ones with the intuitively smallest product: 1/16 and -10.
5. 1/16 * -10 = -10/16 = a negative number greater than -1.
6. We can tell this because 10 is less than 16 (numerator < denominator produces a fraction smaller than 1) and because only one of the numbers is negative. Hence, our answer will be a negative number (less than 0) and will have an absolute value less than 1 (meaning it will be greater than -1).

Therefore, BC.