### Home > A2C > Chapter 3 > Lesson 3.2.3 > Problem3-127

3-127.

Decide which of the following pairs of expressions are equivalent. For those that are not equivalent, determine if there are any values of the variables that would make them equal (in other words, determine if they are sometimes equal). Justify each of your decisions thoroughly.

1. $\left(3x^{2}y\right)^{3} \text{ and } 3x^{6}y ^{3}$

1. $\left(3x^{2}y\right)^{3} \text{ and } 27x^{6}y ^{3}$

1. $\left(3x^{2}y\right)^{3} \text{ and } 27x^{5}y ^{4}$

1. $\left(3xy\right)^{3} \text{ and } 27x^{5}y^{3}$

First, remember that the $3$ is also being cubed.

Remember what happens when a squared variable is being put to a power.

Only the expressions in part (b) are equivalent.

Think about numbers like $0$ and $1$.

The expressions in part (a) are equivalent only when $x = 0$ or $y = 0$.
The expressions in part (c) are equivalent when both $x$ and $y$ are $1$ or when one of the variables is $0$.