Answer:
a = 111
Step-by-step explanation:
Given expression:
[tex]2^3(2^{x+1}+2^{x+4}-2^{x+2}-2^{x-3})[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c[/tex]
[tex]\implies 2^3(2^x \cdot 2^1+2^x \cdot 2^4-2^x \cdot 2^2-2^{x-3})[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{b-c}=\dfrac{a^b}{a^c}[/tex]
[tex]\implies 2^3\left(2^x \cdot 2^1+2^x \cdot 2^4-2^x \cdot 2^2-\dfrac{2^x}{2^3}\right)[/tex]
Simplify:
[tex]\implies 8\left(2^x \cdot 2+2^x \cdot 16-2^x \cdot 4-2^x \cdot \dfrac{1}{8}\right)[/tex]
Factor out [tex]2^x[/tex] :
[tex]\implies 8\left(2^x \left[2+16-4- \dfrac{1}{8}\right]\right)[/tex]
Simplify:
[tex]\implies 8\left(2^x \left[\dfrac{111}{8}\right]\right)[/tex]
[tex]\implies 111 \cdot 2^x[/tex]
Therefore, a = 111
