Simplify rational exponents

[tlcourtney]

x[sup:3jn0igb6]3/2[/sup:3jn0igb6]=125

Please explain how to simplify this problem. :|

 

[mmm4444bot]

Raise both sides to the 2/3 power.

(x^[3/2])^(2/3) = 125^(2/3)

Now use the following property of exponents.

(x^n)^m = x^(n*m)

 

[tlcourtney]

Thanks, I can do that part, but I can't get the next step. I don't know how to simplify a fractional exponent.

 

[mmm4444bot]

… I can do that part …

You did a good job of showing your work, in previous posts.

Are you feeling lazy? :wink:

 

[mmm4444bot]

I just realized that you might be trying to ask how to evaluate 125^(2/3).

Is that it?

 

[tlcourtney]

The book says simplify. The directions "Solve each equation with rational exponents"

 

[mmm4444bot]

\(\displaystyle x^{\frac{3}{2}} = 125\)

\(\displaystyle \left( x^{\frac{3}{2}} \right)^{\frac{2}{3}} = 125^{\frac{2}{3}}\)

\(\displaystyle x = 25\)



If I wrote anything that you do not understand, then please ask specific questions.

 

[tlcourtney]

That is correct BUT how did you get 25. I don't understand the process. Will you please PLEASE break it down for me?

 

[mmm4444bot]

Please tell me which model calculator you're using.

On my calculator, I enter the following.

1 2 5 ^ ( 2 / 3 )

Then I press the [Enter] button.

 

[mmm4444bot]

Does your calculator have a key that looks like this?

\(\displaystyle x \surd y\)

 

[tlcourtney]

Maybe that's my problem, I wasn't using a calculator. I was trying to do it manually.

 

[mmm4444bot]

125 = 5^3

Do you know what the cube root of 5^3 is ?

Square that.

Raising to the 2/3 power represents two operations. Squaring and taking the cube root. They can be done in either order.