Which can be used to describe the expression? Check all that apply.(r -4)3There are three factors of r -4.The expression is equal to 1 over 12 factors of r.Adding the exponents will create an equivalent expression.Multiplying the exponents will create an equivalent expression.The expression simplifies to .

We can write the expression above as the following function:

[tex]f(r)=(r-4)^{3}[/tex]

So let's examine the expressions that are true for this exercise.

1. There are three factors of [tex]r-4[/tex]:

This is true because we can write the function [tex]f(r)[/tex] as follows:

[tex]f(r)=(r-4)(r-4)(r-4)[/tex]

So you can see that in fact there are three factors.

2. The expression is equal to 1 over 12 factors of r.

This is false. It is obvious that this is impossible. There is no any way to get the same expression by applying this statement.

3. Adding the exponents will create an equivalent expression.

This is true because we can write the function as follows:

[tex]f(r)=(r-4)^{1+1+1}[/tex]

So adding one three times we can get the same function, that is:

[tex]1+1+1=3[/tex]

Therefore this is an equivalent expression because:

[tex]f(r)=(r-4)^{1+1+1}=(r-4)^{3}[/tex]

4. Multiplying the exponents will create an equivalent expression.

This is true.You can get the following expression:

[tex]f(r)=(r-4)^{\frac{2}{3}\times \frac{9}{2}}[/tex]

By multiplying the exponents we have:

[tex]\frac{2}{3}\times \frac{9}{2}=3[/tex]

Therefore this is an equivalent expression because:

[tex]f(r)=(r-4)^{\frac{2}{3}\times \frac{9}{2}}=(r-4)^{3}[/tex]

5. The expression simplifies to.

The expression is simplified, that is, it has been factorized. Therefore there is no a way to simplify this function but:

[tex]f(r)=(r-4)^{3}[/tex]