## anonymous 3 years ago okay, so what is the answer to (sqrt10xthirdroot10)^8 ?

1. anonymous

yupp!

2. anonymous

The answer I got was 10,000xsqrt100000000....

3. Kainui
4. anonymous

how did you get the 1,000,000...

5. anonymous

could anyone explain to me how to get the answer..

6. anonymous

Sometimes you might find it easier to work with exponents. Here are the rules$\sqrt{x}=x ^{^{\frac{ 1 }{ 2 }}}$

7. anonymous

mhmmm, so it be (10^1/2x10^1/3)^8

8. anonymous

but what do I do from there?

9. anonymous

You go back to first class of algebra$a ^{m}a ^{n}=a ^{m+n}$$(a ^{m})^{n}=a ^{mn}$

10. anonymous

okay I got 10^20/3......where do I get 1,000,000x10^2/3 from that ?

11. anonymous

That is a computer's 'computation', your teacher wouldn't normally expect that result. But if both you and Wolfram are correct, it is a good way to double check your answer.

12. anonymous

I mean he wouldn't expect it expressed that way.

13. anonymous

.....

14. anonymous

the square root of ten to the power of eight is the same as ten to the power of four

15. anonymous

$$\sqrt{10}^8=10^4=10000$$

16. anonymous

the cubed root of ten to the power of eight is ten squared times the cube root of ten to the second power, because three goes in to eight twice, with a remainder of two

17. anonymous

$\sqrt[3]{10}^8=10^2\sqrt[3]{10^2}=100\sqrt[3]{100}$

18. anonymous

19. anonymous

$1000\times 100\times \sqrt[3]{100}=1,000,000\sqrt[3]{100}$

20. anonymous

Good, now you have two different methods. Last one is a little typo, 1000 should be 10000

Find more explanations on OpenStudy