Question

Which expression is equivalent to 7x , if b > 0?

Answer 1

C.

Explanation:

7x²×sqrt(2x⁴)×6×sqrt(2x¹²)

we see right away that as constant multiplication factor we have 7×6 = 42.

and then we get from each sqrt expression a sqrt(2), which leads to sqrt²(2) = 2 and therefore 42×2=84.

the only answer option with 84 is C.

now, to be completely sure, and to get some practice, let's look at the other parts :

sqrt(2x⁴) = sqrt(2)×sqrt(x⁴) = sqrt(2)×x²

sqrt(2x¹²) = sqrt(2)×sqrt(x¹²) = sqrt(2)×x⁶

=>

7x²×sqrt(2)×x²×6×sqrt(2)×x⁶ =7×6×2×x²×x²×x⁶ = 84x¹⁰

perfect. C is confirmed.

Answer 2

Answer: Choice C

Work Shown:

`7x^2*√(2x^4)*6\sqrt{2x^(12)}\\\\7*6x^2*\sqrt{2x^4*2x^(12)}\\\\42x^2*\sqrt{4x^(4+12)}\\\\42x^2*\sqrt{4x^(16)}\\\\42x^2*√((2x^8)^2)\\\\42x^2*(2x^8)\\\\42*2x^(2+8)\\\\84x^(10)\\\\`

So that's why the answer is choice C

The requirement that x is nonzero isn't technically necessary. The original expression simplifies to choice C even when x = 0 is the case. Also, we don't have issues such as division by zero errors that could arise. It's a bit curious why your teacher put in that condition.