Confusion about Coulomb's Law and 3 Point Charges

[Roodles01]

Homework Statement

2 questions regarding the answer I have been given for this problem. Attachments are the problem & relevant worked answer I disagree with.

Problem
Three charges are arranged in the xy-plane as shown in attachment. A charge Q is at the point A with (x, y) coordinates (–2a, 4a), a charge –Q is at the point B which is the origin (0, 0), and a charge 2Q is at point C with coordinates (3a, 4a).

Find an expression for the force FC on the charge at C due to the other two charges and hence determine the magnitude |FC| of the force and the unit vector that specifies the direction of FC

Homework Equations

Coulomb's law
F = q₁ q₂ / 4 ∏ ε₀ r₁₂³ rhat₁₂

F = ke q₁ q₂ / r₁₂³ * rhat

where ke = 1 / 4 ∏ ε₀

The Attempt at a Solution

F_CA = 1/4∏ε₀ q_C q_A / r_CA³ * r_CA

F_CA = ke 2Q Q / (5a)³ * (5a ex)
OK, but then goes to

F_CA = ke Q2 / a² * 2/5³ * (5a ex)

probably simple algebra but can't see how (5a)³ goes to a² &5³

Next query is regarding
F_CB = ke * 2Q * -Q / (5a)³ * (3aex + 4aey)

How can the denominator be (5a)³ too, surely this is √20
Please assure me (or otherwise) that it's not (5a)³

Thank you

 

[ap123]

probably simple algebra but can't see how (5a)³ goes to a² &5³

There's an "a" in the numerator which leaves a² in the denominator.

How can the denominator be (5a)³ too, surely this is √20

Remember that r_CA is the vector from C to A and is not the position vector of A

 

[Roodles01]

Thank you.
Yes, easy points to remedy.