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AngelaB97
 one year ago
can someone please help me understand radicals??
AngelaB97
 one year ago
can someone please help me understand radicals??

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AngelaB97
 one year ago
Best ResponseYou've already chosen the best response.1dw:1441684069299:dw

AngelaB97
 one year ago
Best ResponseYou've already chosen the best response.1how would you solve this?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\large \sqrt[5]{\frac{1}{8}} \cdot \sqrt[5]{\frac{1}{4}}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Let's start by rewriting this as a fraction with a power. Recall that \(\large \sqrt[n]{x^m} =(x^m)^n\)\[\left(\frac{1}{8}\right)^{1/5}\]Can you tellme how we would write the other fraction?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Awesome. Now we multiply them together. \[\left(\frac{1}{8}\right)^{1/5}\cdot \left(\frac{1}{4}\right)^{1/5}\] Next we distribute the fractional power to all terms within the parenthesis \[\left(\frac{1}{8^{1/5}}\right)\left(\frac{1}{4^{1/5}}\right)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0And now we just multiply.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{1}{8^{1/5} \cdot 4^{1/5}} = \frac{1}{32^{1/5}} \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Now an easy way to think about it is finding the prime factors of 32. What are they?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes, and if we break 8 and 4 down even further, what would we get?

AngelaB97
 one year ago
Best ResponseYou've already chosen the best response.1dw:1441685366603:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Is that a question mark?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1441685422951:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0You're right about the 2, Now let's break 32 apart. \[(32)^{1/5} = (2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2)^{1/5}\] The \(\frac{1}{5}\) power represents the 5th root. This means that for every PAIR of FIVE numbers, 1 will come out of the 5th root. Therefore since there are exactly five 2's under the 5th root, we are going to only use one 2.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Does that make sense, @AngelaB97 ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Therefore \(\dfrac{1}{32^{1/5}} = \boxed{\dfrac{1}{2}}\)

AngelaB97
 one year ago
Best ResponseYou've already chosen the best response.1yes thanks so much once again @Jhannybean

AngelaB97
 one year ago
Best ResponseYou've already chosen the best response.1sorry to bother you again
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