Вычислите 2⁵-(2²)⁶. .⁻⁻⁻⁻⁻⁻⁻⁻. .2¹⁴.

Формулы:
$(a^x)^y=a^{x*y} \\ \frac{a^x}{a^y} =a^{x-y} \\ a^{-x}= \frac{1}{a^x} \\ a^x*a^y=a^{x+y}$

$\frac{2^5-(2^2)^6}{2^{14}} = \frac{2^5-2^{2*6}}{2^{14}} =\frac{2^5-2^{12}}{2^{14}} = \frac{2^5}{2^{14}} -\frac{2^{12}}{2^{14}} =2^{5-14}-2^{12-14}= \\ =2^{-9}-2^{-2}= \frac{1}{2^9} - \frac{1}{2^2}= \frac{1}{512}- \frac{1}{4} = \frac{1}{512} - \frac{128}{512} =- \frac{127}{512}$

$\frac{2^5*(2^2)^6}{2^{14}} = \frac{2^5*2^{2*6}}{2^{14}} =\frac{2^5*2^{12}}{2^{14}} =\frac{2^{5+12}}{2^{14}}=\frac{2^{17}}{2^{14}}=2^{17-14}=2^3=8$