Question

This rational expression is nonequivalent. 5x / 25x^4 ; x^3 / 5x^15
True or false?????

Answer 1

It is nonequivalent. Figure it out this way. Think about what number has to be multiplied by both the numerator and the denominator of
`(5x)/(25x^4)` to get to
`(x^3)/(5x^15)`. It has to be the samee number for the one expression to be equivalent to the other. To get from 5x to x^3, we have to multiply by 1/5x^2. When we do that we get x^3. Good. Now we have to multiply the denominator by the same thing, 1/5x^2.
`25x^4((1)/(5)x^2)=5x^6`. As you can see, they are not equivalent.

Answer 2

For this case we have the following expressions:

`(5x)/(25x^4)`

`(x^3)/(5x^(15))`

We can rewrite both expressions using properties of powers.

For power properties we have:

"In a division, if we have the same base, we subtract the exponents"

Rewriting both expressions we have:

`(5x)/(25x^4) = (1)/(5)x^(1-4) = (1)/(5)x^(-3) = (1)/(5x^3)`

`(x^3)/(5x^(15)) = (1)/(5)x^(3-15) =(1)/(5)x^(-12) = (1)/(5x^(12))`

Answer:

True.

Rational expressions are not equivalent.