Math Snap

STEP 1

Assumptions1. We are dealing with exponential notation.
. The base numbers are the same in each expression.
3. The rules of exponents apply.

STEP 2

The rule of exponents states that when you multiply two powers with the same base, you add the exponents. So, we add the exponents in the expression $2^{-9} \cdot2^{-6}$.
$$2^{-9} \cdot2^{-6} =2^{-9 + (-6)}$$

STEP 3

Now, perform the addition operation in the exponent.
$$2^{-9 + (-6)} =2^{-15}$$

The rule of exponents states that a negative exponent means that the base is on the wrong side of the fraction line, so you flip the base to the other side. So, we rewrite $2^{-15}$ as a fraction with a positive exponent.
$$2^{-15} = \frac{1}{2^{15}}$$This is the simplest form of $2^{-9} \cdot2^{-6}$ with positive exponents.