Question

Simplify (1/2x^2y)^5

Answer 1

Start with

$\left(\dfrac{1}{2}x^2y\right)^5$

We have to raise all terms to the fifth power:

$\left(\dfrac{1}{2}x^2y\right)^5 = \left(\dfrac{1}{2}\right)^5\cdot (x^2)^5\cdot y^5$

Recall the law

$(a^b)^c=a^{bc}$

to conclude that

$\left(\dfrac{1}{2}x^2y\right)^5 = \dfrac{1}{2^5}x^{10}y^5=\dfrac{1}{32}x^{10}y^5$