simplification problem giving trouble: (2(x-4))^3/2)/3 -8(x+4)^1/2

[calc67x]

I have an equation like this:
(2(x-4))^3/2)/3 -8(x+4)^1/2



It appears to simplify to
2/3(x-4)^1/2(x+8)

I have no idea why, however.
Any help with steps is appreciated.
Or even a pointer on how to approach it.

 

[Dr.Peterson]

I have an equation like this:
(2(x-4))^3/2)/3 -8(x+4)^1/2

It appears to simplify to
2/3(x-4)^1/2(x+8)

I have no idea why, however.
Any help with steps is appreciated.
Or even a pointer on how to approach it.

Both terms contain powers of (x-4). Factor out the lower power, (x+4)^(1/2), noting that (x+4)^(3/2) = (x+4)*(x+4)^(1/2).

If you need more help, show your steps so we can check for errors.

 

[mmm4444bot]

I have an e͏quation like this:

(2(x-4))^(3/2))/3 -8(x+4)^(1/2)

Here are some quick notes about terminology and format.

You have not typed an equation. (All equations contain an equal sign.) Call it an expression, instead.

Always type grouping symbols around fractional exponents (or any exponent containing more than a single number).

Also, your expression has mismatched grouping symbols (i.e., only 3 open-parentheses but 4 close parentheses).

Corrected: (2(x - 4))^(3/2)/3 - 8(x + 4)^(1/2)