Here's the question you clicked on:
christinaxxx
okay, so what is the answer to (sqrt10xthirdroot10)^8 ?
The answer I got was 10,000xsqrt100000000....
http://www.wolframalpha.com/input/?i=(sqrt10xthirdroot10)%5E8&t=crmtb01
how did you get the 1,000,000...
could anyone explain to me how to get the answer..
Sometimes you might find it easier to work with exponents. Here are the rules\[\sqrt{x}=x ^{^{\frac{ 1 }{ 2 }}}\]
mhmmm, so it be (10^1/2x10^1/3)^8
but what do I do from there?
You go back to first class of algebra\[a ^{m}a ^{n}=a ^{m+n}\]\[(a ^{m})^{n}=a ^{mn}\]
okay I got 10^20/3......where do I get 1,000,000x10^2/3 from that ?
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.
I mean he wouldn't expect it expressed that way.
the square root of ten to the power of eight is the same as ten to the power of four
\(\sqrt{10}^8=10^4=10000\)
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
\[\sqrt[3]{10}^8=10^2\sqrt[3]{10^2}=100\sqrt[3]{100}\]
multiply those together for your answer
\[1000\times 100\times \sqrt[3]{100}=1,000,000\sqrt[3]{100}\]
Good, now you have two different methods. Last one is a little typo, 1000 should be 10000