simplifying w/ fractional exponents: (a - b)^3/2

[ivandoig]

I need to get the expression (a-b)^3/2 in the form b^x * ((a/b)-1)^3/2

what is x? 1 or 3/2? or ?

for clarity: x is exponent on b when b is factored out.

thanks

 

[stapel]

I need to get the expression (a-b)^3/2 in the form b^x * ((a/b)-1)^3/2

I wouldn't say that this is "simplifying" the original expression at all, though it is a rearrangement of sorts.... :shock:

Since b divided by b is 1 and a divided by b is a/b, it would appear that perhaps a good first step might be to multiply (inside the radical) by b/b. The numerator can come out of the radical, and the denominator divided into what's left inside. :idea:

What do you end up with as the power on b outside the radical? :wink:

Eliz.

 

[pka]

\(\displaystyle (a^x)(b^x)=(ab)^x\) so \(\displaystyle x=\frac{3}{2}\).