Question

Consider the expression ab2 and a2b2. Are the two expressions equivalent? Which properties did you use to prove or disprove the equivalency?

Answer 1

Let

$x=ab^{2} \\ y=a^{2}b^{2}$

we know that

if x and y are equivalent

then

$\frac{x}{y} =1$

so

Divide the value of x by y

$\frac{x}{y} = \frac{ab^{2}}{a^{2}b^{2}}= \frac{1}{a} \\\\ \frac{1}{a} \neq 1$

therefore

The expressions are not equivalent