1. AngelaB97

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2. AngelaB97

how would you solve this?

3. AngelaB97

@Jhannybean

4. anonymous

$\large \sqrt[5]{\frac{1}{8}} \cdot \sqrt[5]{\frac{1}{4}}$

5. anonymous

Let's start by rewriting this as a fraction with a power. Recall that $$\large \sqrt[n]{x^m} =(x^m)^n$$$\left(\frac{1}{8}\right)^{1/5}$Can you tellme how we would write the other fraction?

6. AngelaB97

(1/4) ^1/5

7. anonymous

Awesome. Now we multiply them together. $\left(\frac{1}{8}\right)^{1/5}\cdot \left(\frac{1}{4}\right)^{1/5}$ Next we distribute the fractional power to all terms within the parenthesis $\left(\frac{1}{8^{1/5}}\right)\left(\frac{1}{4^{1/5}}\right)$

8. anonymous

And now we just multiply.

9. anonymous

$\frac{1}{8^{1/5} \cdot 4^{1/5}} = \frac{1}{32^{1/5}}$

10. anonymous

Now an easy way to think about it is finding the prime factors of 32. What are they?

11. AngelaB97

8 and 4?

12. anonymous

Yes, and if we break 8 and 4 down even further, what would we get?

13. AngelaB97

|dw:1441685366603:dw|

14. anonymous

Is that a question mark?

15. anonymous

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16. AngelaB97

question mark lol

17. anonymous

Ok haha.

18. anonymous

You're right about the 2, Now let's break 32 apart. $(32)^{1/5} = (2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2)^{1/5}$ The $$\frac{1}{5}$$ power represents the 5th root. This means that for every PAIR of FIVE numbers, 1 will come out of the 5th root. Therefore since there are exactly five 2's under the 5th root, we are going to only use one 2.

19. anonymous

Does that make sense, @AngelaB97 ?

20. anonymous

Therefore $$\dfrac{1}{32^{1/5}} = \boxed{\dfrac{1}{2}}$$

21. AngelaB97

yes thanks so much once again @Jhannybean

22. AngelaB97

sorry to bother you again

23. anonymous

No problem :)