Question

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

Answer 1

111

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

a = 111

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)=(a^b)/(a^c)`

`\implies 2^3\left(2^x \cdot 2^1+2^x \cdot 2^4-2^x \cdot 2^2-(2^x)/(2^3)\right)`

Simplify:

`\implies 8\left(2^x \cdot 2+2^x \cdot 16-2^x \cdot 4-2^x \cdot (1)/(8)\right)`

Factor out
`2^x` :

`\implies 8\left(2^x \left[2+16-4- (1)/(8)\right]\right)`

Simplify:

`\implies 8\left(2^x \left[(111)/(8)\right]\right)`

`\implies 111 \cdot 2^x`

Therefore, a = 111