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 $\frac{5x}{25x^4}$ to get to $\frac{x^3}{5x^15}$. 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. $25x^4(\frac{1}{5}x^2)=5x^6$. As you can see, they are not equivalent.

Answer 2

For this case we have the following expressions:

$\frac{5x}{25x^4}$

$\frac{x^3}{5x^{15}}$

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:

$\frac{5x}{25x^4} = \frac{1}{5}x^{1-4} = \frac{1}{5}x^{-3} = \frac{1}{5x^3}$

$\frac{x^3}{5x^{15}} = \frac{1}{5}x^{3-15} =\frac{1}{5}x^{-12} = \frac{1}{5x^{12}}$

Answer:

True.

Rational expressions are not equivalent.