Question

simplify this expression, wrote the answer with positive exponents only.

Answer 1

Given the expression:

$(xy^3)^2(x^2y)^{-1}$

for the left factor, we can multiply the exponents to get the following:

$(xy^3)^2=x^2y^{3\cdot2}=x^2y^6$

and the right factor can be written like this:

$(x^2y)^{-1}=\frac{1}{x^2y}$

if we combine these results on the original expression, we get:

$(xy^3)^2(x^2y)^{-1}=(x^2y^6)\cdot\frac{1}{x^2y}=\frac{x^2y^6}{x^2y}=y^5$

therefore, the simplified expression is y⁵