Question

consider the expressions ab^2 and a^2 b^2 . are the two expressions equivalent? which properties did you use to prove or disprove the equivalency

Answer 1

Answer: No, they are not equivalent.

Step-by-step explanation:

Since we have given that

$ab^2\ and\ a^2b^2$

No, the two expressions are not equivalent.

As we know that

$a^2b^2$ can be written as $(ab)^2$

but $ab^2$ can't be written as that .

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

Suppose if they are equivalent then,

then, $x=y\\\\dfrac{x}{y}=1$

So, if we put the values of x and y we get that

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

Hence, they are not equivalent.

Answer 2

Yes,distributive property