Start with
[tex]\left(\dfrac{1}{2}x^2y\right)^5[/tex]
We have to raise all terms to the fifth power:
[tex]\left(\dfrac{1}{2}x^2y\right)^5 = \left(\dfrac{1}{2}\right)^5\cdot (x^2)^5\cdot y^5[/tex]
Recall the law
[tex](a^b)^c=a^{bc}[/tex]
to conclude that
[tex]\left(\dfrac{1}{2}x^2y\right)^5 = \dfrac{1}{2^5}x^{10}y^5=\dfrac{1}{32}x^{10}y^5[/tex]
