Question

Can someone help
me with this and explain how you got it?

Answer 1

Answer:

111

Step-by-step explanation:

2^3[2^(x+1) + 2^(x+4) - 2^(x+2) - 2^(x-3)] =

2^(x+4) + 2^(x+7) - 2^(x+5) - 2^x =

2^x (2^4 + 2^7 - 2^5 -1) =

2^x (16+128-32-1) =

2^x (111) =

111 × 2^x = a × 2^x

so, the value of a = 111

Answer 2

Answer:

a = 111

Step-by-step explanation:

Given expression:

$2^3(2^{x+1}+2^{x+4}-2^{x+2}-2^{x-3})$

$\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c$

$\implies 2^3(2^x \cdot 2^1+2^x \cdot 2^4-2^x \cdot 2^2-2^{x-3})$

$\textsf{Apply exponent rule} \quad a^{b-c}=\dfrac{a^b}{a^c}$

$\implies 2^3\left(2^x \cdot 2^1+2^x \cdot 2^4-2^x \cdot 2^2-\dfrac{2^x}{2^3}\right)$

Simplify:

$\implies 8\left(2^x \cdot 2+2^x \cdot 16-2^x \cdot 4-2^x \cdot \dfrac{1}{8}\right)$

Factor out $2^x$ :

$\implies 8\left(2^x \left[2+16-4- \dfrac{1}{8}\right]\right)$

Simplify:

$\implies 8\left(2^x \left[\dfrac{111}{8}\right]\right)$

$\implies 111 \cdot 2^x$

Therefore, a = 111