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## anonymous one year ago help

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1. anonymous

sqrt[6]{125a^15}

2. anonymous

with what

3. anonymous

$\sqrt[6]{125a^1}$

4. anonymous

a^15 my bad

5. anonymous

$\sqrt{5} ^15 6. Nnesha convert 6th root to exponent \[\huge\rm \sqrt[n]{x^m} = x^\frac{ m }{ n }$

7. anonymous

$\sqrt[5]{15}$

8. anonymous

like this

9. Nnesha

nope it's 6th root so n = 6 |dw:1433351042568:dw| so $\huge\rm \sqrt[6]{a^{15}} = a^\frac{ ? }{ ? }$

10. anonymous

a^15/6

11. Nnesha

yep right now reduce the fraction

12. anonymous

5/2

13. anonymous

so a 5/2 is the answer

14. anonymous

nope

15. Nnesha

not done a^5/2 $\huge\rm a^\frac{ a \times a \times a \times a \times a }{ a \times a }$ can u cancel out 2 a's or in other words how many times 2 goes into 5 ?

16. anonymous

2

17. anonymous

times

18. Nnesha

yep right so 5/2 2 times so 4-5 = 1 that's mean a stay under the root and one a^2 u can write it outside the root |dw:1433351567387:dw| now factor 125

19. Nnesha

5^what power =125 ?

20. Nnesha

a^5/2 can be written as $\huge\rm \sqrt{a^5} = \sqrt{a^2 \times a^2 \times a}$ (when we multiply same bases we should add their exponent ) square cancels with square root so $a \times a \sqrt{a} = a^2 \sqrt{a}$

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