Answer
$a.$
$y^{6}=y^{1+5}=y^{1}\cdot y^{5}$
$y^{6}=y^{2+4}=y^{2}\cdot y^{4}$
$y^{6}=y^{3+3}=y^{3}\cdot y^{3}$
$y^{6}=y^{4+2}=y^{4}\cdot y^{2}$
$b.$
$y^{6}=y^{8-2}=y^{8}\cdot y^{-2}$
$y^{6}=y^{10-4}=y^{10}\cdot y^{-4}$
$y^{6}=y^{100-94}=y^{100}\cdot y^{-94}$
$y^{6}=y^{1000-994}=y^{1000}\cdot y^{-994}$
$c.$
There are infinitely many ways to obtain 6 adding a positive a negative number (see part b).
So, we can write $y^{6}$ as a product of two powers in an infinite number of ways.
Work Step by Step
Given above.
