Rational Exponents and Radicals: simplification

[will7675]

All of these exponents that are fraction form confuse me!

Problem 1: Simplify:

6^1/5 * 6^3/5

I tried using the TeX format to do the exponents,but because they are fractions, it did not look right. So, in this problem, the exponents are the fractions 1/5 and 3/5, and the ^is the "raised to"symbol

I multiplied 6 and 6 to get 36. Then I added the exponents to get 4/5, and a final answer of 36^4/5. BUT I did not know if I should go further by taking 36^4/5 to get the big number of 335923.2!?! I thought that when there is no letter variable, you go ahead and simplify it all the way. So should I leave it as 36^4/5 or take it further?

Problem 2: Simplify: (7x^3) / (4x^(3/4))

(that is supposed to look like a division/fraction problem!)
Once again, I do not know how to do the TeX symbol for the fraction/division sign, so please do not chew me out! I'm very new to this whole thing, and everyone has to learn for the first time somewhere.

I subtracted the exponents and got 2.25, Then you can't easily divide 7 by 4, so i left the 7/4 and got an answer of 7/4^9/4 which looks wrong and confusing to me, so I did it another way and got a different answer:

I did 7 divided by four and got 1.75, and some some reason added it to the 2.25 i got from subtracting the exponents. That gave me the answer of 4x. Which is probably wrong..ahh help!

Thanks guys and gals, if you can help me out!

 

[galactus]

Problem 1:Simplify:

6^1/5 * 6^3/5

I multiplied 6 and 6 to get 36. Then I added the exponents to get 4/5, and a final answer of 36^4/5. BUT I did not know if I should go further by taking 36^4/5 to get the big number of 335923.2!?! I thought that when there is no letter variable, you go ahead and simplify it all the way. So should I leave it as 36^4/5 or take it further?

Merely add your exponents: 1/5+3/5=4/5. \(\displaystyle 6^{\frac{1}{5}}\cdot{6^{\frac{3}{5}}}=6^{\frac{4}{5}}\)

Problem 2: Simplify: (7x^3) / (4x^(3/4))

I subtracted the exponents and got 2.25, Then you can't easily divide 7 by 4, so i left the 7/4 and got an answer of 7/4^9/4 which looks wrong and confusing to me, so I did it another way and got a different answer:
I did 7 divided by four and got 1.75, and some some reason added it to the 2.25 i got from subtracting the exponents. That gave me the answer of 4x. Which is probably wrong..ahh help!

Remember, when you divide exponents, you subtract them. 3-3/4=9/4.

Therefore, \(\displaystyle \frac{7^{3}}{4x^{\frac{3}{4}}}=\frac{7x^{\frac{9}{4}}}{4}\)

That wasn't so hard, was it?. Have fun. Practice. Pretty soon, laws of exponents will be second nature.

 

[soroban]

Re: Rational Exponents and Radicals

Hello, Lauren!

Problem 1. Simplify: 6^1/5 * 6^3/5

I tried using the TeX format to do the exponents,
but because they are fractions, it did not look right.

You may have typed: 6^1/5 and it came out: \(\displaystyle \,6^1/5\)


If the exponent has more than one character, it must be enclosed in braces, { }

Then 6^{1/5} will give us: \(\displaystyle \,6^{1/5}\)


Fractions can be typed with \frac{1}{5}: \(\displaystyle \,\frac{1}{5}\)

So that 6^{\frac{1}{5}} will give us: \(\displaystyle \,6^{\frac{1}{5}}\)