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

1. christinaxxx Group Title

yupp!

2. christinaxxx Group Title

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

3. Kainui Group Title
4. christinaxxx Group Title

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

5. christinaxxx Group Title

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

6. chaguanas Group Title

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

7. christinaxxx Group Title

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

8. christinaxxx Group Title

but what do I do from there?

9. chaguanas Group Title

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

10. christinaxxx Group Title

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

11. chaguanas Group Title

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 Group Title

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

13. christinaxxx Group Title

.....

14. satellite73 Group Title

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

15. satellite73 Group Title

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

16. satellite73 Group Title

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 Group Title

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

18. satellite73 Group Title

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