# Thread: Simplify surds and powers.

1. ## Simplify surds and powers.

I have no idea how to do these. Help would be nice.

3√27x^6y^9

5√8a^7c^11

2. You want to graph these?

Is the first equation $\displaystyle \displystyle \sqrt[3]{27}x^6y^9$ or $\displaystyle \displyatyle 3\sqrt{27}x^6y^9$ ?

3. Sorry i didnt clarify. It says to simplify them.

both problems are written like the first example you typed.(little 3).
then the second problem has a (little 5) outside the root symbol.

4. $\displaystyle \displaystyle \sqrt[3]{27} = 3$ as $\displaystyle \dispalystyle 3^3 = 27$

Does this make sense?

5. yes? =) im sorry i seem so unbright...im not that great in mathematics.

6. I'm starting to think your equation is $\displaystyle \displaystyle \sqrt[3]{27x^6y^9}$ ?

7. yes sir..thats what my homework paper says..i just have to simplify it...and i dont know how to do that.

8. Firstly \$\displaystyle \displaystyle \sqrt[3]{27x^6y^9} = \sqrt[3]{27}\times \sqrt[3]{x^6}\times \sqrt[3]{y^9}$

Now recall that $\displaystyle \displaystyle \sqrt[n]{a} = a^{\frac{1}{n}}$

Re-write the equation using this rule.

9. mk. thnks

10. I get $\displaystyle \displaystyle \sqrt[3]{27}\times \sqrt[3]{x^6}\times \sqrt[3]{y^9} = 27^{\frac{1}{3}}x^{6\times {\frac{1}{3}}}\times y^{9\times {\frac{1}{3}}}$

Simplify this..