Solving Exponential Equations: Need Help Understanding 2 Questions

[linapril]

I need help with understanding two questions:
1. (2^x+2)²
The answer I got was: 2^2x+2^x++4, but according to the answers that is wrong. Can any explain why?

2. 8^4x/32^x
I simplified this to become (8⁴/32)^x, but I don't know how to go from there... The answer is apparently 2^7x, but I don't understand how that can be...

Would appreciate the help enormously,
//APRIL

 

[linapril]

Nevermind, I understood question 2 now, but question 1 is still a mystery to me...

 

[Jameson]

I need help with understanding two questions:
1. (2^x+2)²
The answer I got was: 2^2x+2^x++4, but according to the answers that is wrong. Can any explain why?

I think the middle term is wrong. The first and the last terms look good though. Check your work and if you still don't see it then post your attempt and we'll help you sort it out :)

 

[Prove It]

I need help with understanding two questions:
1. (2^x+2)²
The answer I got was: 2^2x+2^x++4, but according to the answers that is wrong. Can any explain why?

2. 8^4x/32^x
I simplified this to become (8⁴/32)^x, but I don't know how to go from there... The answer is apparently 2^7x, but I don't understand how that can be...

Would appreciate the help enormously,
//APRIL

$\displaystyle \begin{align*} \left( 2^x + 2 \right)^2 &= \left( 2^x \right)^2 + 2\cdot 2\cdot 2^x + 2^2 \\ &= 2^{2x} + 2^{x + 2} + 2^2 \end{align*}$

 

[CellCoree]

Hello April,

I can definitely help you understand these two questions about solving exponential equations.

First, let's take a look at the first question: (2x+2)^2. The answer you got, 22x+2x++4, is incorrect. When you have an exponential expression raised to a power, you need to use the exponent rule that states (a^b)^c = a^(b*c). In this case, that means we can rewrite the expression as (2x+2)(2x+2). Now, we can use the distributive property to simplify this further. We multiply the first term (2x) by both terms in the second parentheses (2x and 2) and then multiply the second term (2) by both terms in the second parentheses (2x and 2). This gives us 4x^2 + 4x + 4x + 4, which simplifies to 4x^2 + 8x + 4. Therefore, the correct answer is 4x^2 + 8x + 4.

Moving on to the second question: 84x/32x. You correctly simplified this to (84/32)x. Now, we need to simplify the fraction 84/32. We can do this by finding the greatest common factor (GCF) of both numbers, which is 4. We divide both numbers by 4 to get 21/8. Therefore, the expression becomes (21/8)x. And since 21 and 8 have no common factors, we cannot simplify this any further. The answer is simply (21/8)x or 2.625x.

I hope this explanation helps you understand how to solve these types of exponential equations. If you have any further questions, don't hesitate to ask. Keep up the good work!