## College Algebra (6th Edition)

$\frac{1}{16}$
When dividing exponential expressions with the same non-zero base, subtract the exponent of the denominator from the exponent of the numerator and give the resulting exponent to the same base: $$\frac{2^{3}}{2^{7}}$$ $$=2^{(3-7)}$$ $$=2^{(-4)}$$ When an exponential expression has a negative exponent, change the position of the base (from the numerator to the denominator, or vise-versa) and make the exponent positive. $$=\frac{1}{2^{4}}$$ $$=\frac{1}{16}$$