SOLUTION: A very pleasant evening to you Math Solvers! I am encountering some difficulties about radicals, can you please help me. In my problems it is specified that you just need to simpli
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Question 120761: A very pleasant evening to you Math Solvers! I am encountering some difficulties about radicals, can you please help me. In my problems it is specified that you just need to simplify the following by reducing as much as possible, here it follows:
->cube root of 1000 x^6 y^5
Thank you very much!!!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given expression
^{\frac{1}{3}})
Convert the expression from radical notation to exponent notation. Remember 
^1x^6y^5\right)^{\frac{1}{3}})
Rewrite 1000 as
^{1\left(\frac{1}{3}\right)}x^{6\left(\frac{1}{3}\right)}y^{5\left(\frac{1}{3}\right)})
Now distribute the exponent Now distribute the outer exponent to each exponent in the parenthesis. Remember
^{\frac{1}{3}}x^{\frac{6}{3}}y^{\frac{5}{3}})
Now multiply the exponents
^{\frac{1}{3}}x^{2}y^{\frac{5}{3}})
Reduce
Now convert back to radical notation
Take the cube root of 1000 to get 10
So simplifies to
In other words, 
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