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## TheYankee one year ago Higher roots with exponents?

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1. TheYankee

How do I simplify?

2. Nnesha

factor x^{16} remember exponent rules $\huge\rm x^m \times x^n = x^{m+n}$

3. Nnesha

so you can write x^5 times x^5 times x^5 times x which is equal to ??

4. Nnesha

$\huge\rm x^5 \times x^5 \times x^5 \times x= x^?$

5. Nnesha

when we multiply same bases we should add their exponents :-) exponent rules $\huge\rm x^m \times x^n = x^{m+n}$

6. TheYankee

So, would it look like this?

7. Nnesha

$\huge\rm x^5 \times x^5 \times x^5 \times x= x^?$ you didn't answer my question :(

8. TheYankee

Wouldn't it be x^16? (I have such a problem with these >.< )

9. Nnesha

yes right

10. Nnesha

now factor them under the 5th root $\huge\rm \sqrt[5]{x^5 \times x^5 \times x^5 \times x }$ just like square can cancelz out with square same idea here &that's why we have to make a pair of five exponent so we cancel them with 5th root solve that

11. Nnesha

you can convert root to exponent $\huge\rm \sqrt[n]{x^m}= x^\frac{ m }{ n }$

12. TheYankee

Oh! Alright! I didn't know that! (Please excuse my ineptitude... I'm a history person, lol....)

13. TheYankee

Huh! Would it be X^4, then?

14. Nnesha

convert 5th root to exponent

15. TheYankee

When you convert to an exponent, Each 5th root would result in one, correct? Making it just X instead of x rasied to a power.

16. Nnesha

yes right but x is same as x to the one power x^1

17. TheYankee

True. So because each x factor would result in x^1, I'm thinking the end result would be X^4.

18. Nnesha

$\huge\rm \sqrt[5]{x^5 \times x^5 \times x^5 \times x }$ $\huge\rm x^\frac{5 }{ 5 } \times x^\frac{ 5 }{ 5 } \times x^\frac{ 5 }{ 5 } \times x^\frac{ 1 }{ 5 }$ so it should be like this

19. Nnesha

$\huge\rm \sqrt[5]{x^5 \times x^5 \times x^5 \times\color{reD}{ x} }$ red x doesn't have power so you cannot cancel 5th root. it should stay under the 5th rot $\huge\rm x^\frac{5 }{ 5 } \times x^\frac{ 5 }{ 5 } \times x^\frac{ 5 }{ 5 } \times x^\frac{ 1 }{ 5 }$ so it should be like this

20. TheYankee

Omg! It makes sense now! Would it be x^3 5^(sqrt) x? (I'll model that answer in a second. Thanks for your patience ^^)

21. Nnesha

yes!

22. Nnesha

np :-)

23. TheYankee

To confirm, like this?

24. Nnesha

yes

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