1. ## Simplify

Simplify using the law of rational exponents?

1)³√8c^8
2)^5√-96x^25y^12
3)√40r^5t^3s^8

2. Originally Posted by mj.alawami
Simplify using the law of rational exponents?

1)³√8c^8
2)^5√-96x^25y^12
3)√40r^5t^3s^8

Hi mj,

1) $\displaystyle \sqrt[3]{8c^8}=\sqrt[3]{2^3c^3c^3c^2}=2c\cdot c\sqrt[3]{c^2}=2c^2\sqrt[3]{c^2}$

Using rational exponents:

$\displaystyle (2^3)^{1/3}c^{8/3}=2c^{8/3}$

3. Originally Posted by mj.alawami
Simplify using the law of rational exponents?

1)³√8c^8
2)^5√-96x^25y^12
3)√40r^5t^3s^8

3) $\displaystyle \sqrt{40r^5t^3s^8}=\sqrt{4 \cdot 10 \cdot r^4 \cdot r \cdot t^2 \cdot t \cdot s^8}=2r^2s^4t\sqrt{10rt}$

Using rational exponents:

$\displaystyle \sqrt{40r^5t^3s^8}=\sqrt{4 \cdot 10 \cdot r^5 \cdot t^3 \cdot s^8}=(2^2)^{1/2}\cdot 10^{1/2} \cdot r^{5/2} \cdot t^{3/2} \cdot s^{8/2}=2 \cdot 10^{1/2} \cdot r^{5/2} \cdot t^{3/2} \cdot s^4$

4. Originally Posted by masters
Hi mj,

1) $\displaystyle \sqrt[3]{8c^8}=\sqrt[3]{2^3c^3c^3c^2}=2c\cdot c\sqrt[3]{c^2}=2c^2\sqrt[3]{c^2}$
Can my simplifying be

2c^8/3

5. Originally Posted by mj.alawami
Simplify using the law of rational exponents?

1)³√8c^8
2)^5√-96x^25y^12
3)√40r^5t^3s^8

I'm going to guess that you mean this:

2) $\displaystyle \sqrt[5]{-96x^{25}y^{12}}=\sqrt[5]{-32 \cdot 3 \cdot x^{25} \cdot y^{12}}=-2x^5y^2\sqrt[5]{3y^2}$

Using rational exponents:

$\displaystyle \sqrt[5]{-96x^{25}y^{12}}=\sqrt[5]{-32 \cdot 3 \cdot x^{25} \cdot y^{12}}=-2 \cdot 3^{1/5}x^5y^{12/5}$

6. Originally Posted by mj.alawami
Can my simplifying be

2c^8/3
Sorry mj,

I failed to read your initial instructions. You want to use rational exponents not radicals. You are correct for your first one. I will redo my post so that it uses rational exponents.

7. [quote=mj.alawami;256717]

-2* ^5√3 * x^5 * y^2 ^5√y^2

8. Originally Posted by masters
Sorry mj,

I failed to read your initial instructions. You want to use rational exponents not radicals. You are correct for your first one. I will redo my post so that it uses rational exponents.
hey,dont bother about me i will get it ,by the way thank you for taking the time to read my question

9. [quote=mj.alawami;256724]
Originally Posted by mj.alawami

-2* ^5√3 * x^5 * y^2 ^5√y^2
mj,

I don't think you want to mix radicals and rational exponents. I have modified my posts to show rational exponents. Have a look. See if you have any questions about them.

10. [quote=masters;256738]
Originally Posted by mj.alawami

mj,

I don't think you want to mix radicals and rational exponents. I have modified my posts to show rational exponents. Have a look. See if you have any questions about them.
Thank you very much ,you really have helped me alot and no more question for today X|