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christinaxxx Group Title okay, so what is the answer to (sqrt10xthirdroot10)^8 ? one year ago one year ago

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1. christinaxxx

yupp!

2. christinaxxx

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

3. Kainui
4. christinaxxx

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

5. christinaxxx

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

6. chaguanas

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

7. christinaxxx

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

8. christinaxxx

but what do I do from there?

9. chaguanas

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

10. christinaxxx

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

11. chaguanas

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. chaguanas

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

13. christinaxxx

.....

14. satellite73

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

15. satellite73

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

16. satellite73

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. satellite73

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

18. satellite73

multiply those together for your answer

19. satellite73

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

20. chaguanas

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