QuestionSimplify these expressions using positive exponents: a. $2^{-9} \cdot 2^{-6}$, b. $2^{9} \cdot 2^{6}$, c. $5^{15} \div 5^{3}$, d. $5^{15} \div 5^{-3}$, e. $(-3)^{-2}$, f. $\frac{b^{2}}{b^{-3}}$.

Studdy Solution
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.