Expand? #(a^2+b^2)^(3/2)#

1 Answer

Answer:

#(a^2+b^2)sqrt(a^2+b^2)#

Explanation:

#(a^2+b^2)^(3/2)#

The fractional power #3/2# says that we're going to cube the expression (the 3) and then take the square root (the 2). So let's do that:

#sqrt((a^2+b^2)(a^2+b^2)(a^2+b^2))#

Since #(a^2+b^2)(a^2+b^2)=(a^2+b^2)^2#, we can write:

#sqrt((a^2+b^2)^2(a^2+b^2))#

taking the square root:

#(a^2+b^2)sqrt(a^2+b^2)#

Can we go further than this? No - the addition of the #a^2# and #b^2# terms means we can't simply take the square root of each piece.