# Thread: properties of exponents to simplify expressions. help needed.

1. ## properties of exponents to simplify expressions. help needed.

hello there. so i took precalculus in 10th grade, like 3 years ago, and now it's coming back to haunt me on my math placement for college which i have to take in a few days. I'm having a hard time remembering things so if someone could just please help me out i'd greatly appreciate it.

use the properties of exponents to simplify the expression:

i already know the answer is Y/X, but i don't know how to get it.

2. Originally Posted by rafaeli
hello there. so i took precalculus in 10th grade, like 3 years ago, and now it's coming back to haunt me on my math placement for college which i have to take in a few days. I'm having a hard time remembering things so if someone could just please help me out i'd greatly appreciate it.

use the properties of exponents to simplify the expression:

{X^(3/4), Y^(1/2)}
------------------- that whole expression raised to the -2.
X^(1/4), Y

i already know the answer is Y/X, but i don't know how to get it.
$\displaystyle \left(\dfrac{x^{\frac34} y^{\frac12}}{x^{\frac14}y}\right)^{-2}$

Use the rule $\displaystyle \frac{x^a}{x^b} = x^{a-b}$,

$\displaystyle \left(\dfrac{x^{\frac34} y^{\frac12}}{x^{\frac14}y}\right)^{-2}$$\displaystyle = (x^{\frac34- \frac14} y^{\frac12 - 1})^{-2} = (x^{\frac12} y^{-\frac12})^{-2} =$$\displaystyle \left(\frac{x^{\frac12}}{y^{\frac12}}\right)^{-2}$

Now lets use the rule $\displaystyle \frac{x^a}{y^a} = \left(\frac{x}{y}\right)^a$

$\displaystyle \left(\frac{x^{\frac12}}{y^{\frac12}}\right)^{-2}= \left(\left(\frac{x}{y}\right)^{\frac12}\right)^{-2}$

And finally lets use the rule: $\displaystyle (x^a)^b = x^{ab}$

$\displaystyle \left(\left(\frac{x}{y}\right)^{\frac12}\right)^{-2} =\left(\frac{x}{y}\right)^{-2 . \frac12}=\left(\frac{x}{y}\right)^{-1} = \frac{y}{x}$