## DJJo one year ago Will give medal! How do I simplify the square root of the fourth root of 8 in exponential form?

1. DJJo

2. anonymous

$\sqrt{\sqrt[4]{8}}=\sqrt{8^{\frac{ 1 }{ 4}}}=(8^{\frac{ 1 }{ 4 }})^{\frac{ 1 }{ 2 }}=8^{\frac{ 1 }{ 8}}=(2^{3})^{\frac{ 1 }{ 8 }}=2^{\frac{ 3 }{ 8 }}$

3. DJJo

But I'm confused on how you got that @peachpi

4. anonymous

how is it confusing? things to power are multiplied with each other

5. anonymous

square root is the same as the exponent ½ fourth root is exponent ¼

6. DJJo

oh ok thank you @peachpi

7. DJJo

@peachpi Would you mind if I ask you another question?

8. anonymous

ok

9. DJJo

How would I simply this expression in exponential form?

10. anonymous

ok. this is the same type of problem. How would you write the numerator with an exponent?

11. DJJo

3 and 1/2

12. anonymous

exponents with bases being divided are subtracted eg. 3^(1/2) / 3^(1/4) = 3^ ((1/2) - (1/4))

13. anonymous

Yeah. Then √3 is also a part of the denominator so you can do this |dw:1434904015717:dw|

14. DJJo

So would the denominator be 3 and 1/8?

15. anonymous

no... 3 and 1/4

16. anonymous

It would be 3^(1/4) because 1/2 * 1/2 = 1/4

17. anonymous

|dw:1434904157793:dw|

18. anonymous

Now since the base is 3 on top and bottom you can subtract the exponents

19. anonymous

1/4 since as I have explained before... exponents, with bases same being multiplied, are added

20. anonymous

|dw:1434904205322:dw|

21. DJJo

So 3 and 1/4 would be the answer right?

22. anonymous

3 TO THE 1/4

23. DJJo

Yeah, that's what meant Thank you sooooo much @peachpi

24. anonymous

you're welcome