By applying power properties we conclude that the trascendental expression [tex]\frac{2^{x+5}-2\cdot 2^{x+3}-4\cdot (2^{x+1})-6\cdot 2^{x-1}}{2^{x+4}+36\cdot (2^{x-2})}[/tex] is simplified into the rational expression [tex]\frac{5}{24}[/tex].
How to simplify an exponential function
Exponential functions are trascendental functions, these are, expressions that cannot be described algebraically. In this question we must apply power properties to simplify the entire expression. We must use the following properties to simplify the expression:
- [tex]\frac{2^{x+5}-2\cdot 2^{x+3}-4\cdot (2^{x+1})-6\cdot 2^{x-1}}{2^{x+4}+36\cdot (2^{x-2})}[/tex] Given
- [tex]\frac{2^{x+5}-2^{x+4}-2^{x+3}-3\cdot 2^{x}}{2^{x+4}+3^{2}\cdot 2^{x}}[/tex] [tex]a^{m+n} =a^{m}\cdot a^{n}[/tex]/-a = (-1) · a
- [tex]\frac{2^{x}\cdot (2^{5}-2^{4}-2^{3}-3)}{2^{x}\cdot (2^{4}+3^{2})}[/tex] [tex]a^{m+n} =a^{m}\cdot a^{n}[/tex]/Distributive property
- [tex]\frac{2^{5}-2^{4}-2^{3}-3}{2^{4}+2^{3}}[/tex] [tex]\frac{a\cdot b}{c\cdot d} = \frac{a}{b}\cdot \frac{c}{d}[/tex]/Existence of multiplicative inverse/Modulative property/Definition of division
- [tex]\frac{2^{3}\cdot (2^{2}-2-1)-3}{2^{3}\cdot (2+1)}[/tex] [tex]a^{m+n} =a^{m}\cdot a^{n}[/tex]/Distributive property
- [tex]\frac{8\cdot (4-2-1)-3}{8\cdot 3}[/tex] Definition of power/Definition of addition
- [tex]\frac{8-3}{24}[/tex] Definitions of subtraction and multiplication/Modulative property
- [tex]\frac{5}{24}[/tex] Definition of subtraction/Result
By applying power properties we conclude that the trascendental expression [tex]\frac{2^{x+5}-2\cdot 2^{x+3}-4\cdot (2^{x+1})-6\cdot 2^{x-1}}{2^{x+4}+36\cdot (2^{x-2})}[/tex] is simplified into the rational expression [tex]\frac{5}{24}[/tex].
To learn more on exponential functions: https://brainly.com/question/15352175
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