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

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Answer 1 · 2017-01-06T15:35:53

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

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

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.

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