SOLUTION: Simplify {{{root(3,162a^10b^5)/root(3,6a^8b^4)}}}

Question 126506: Simplify

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given expression

First let's simplify the numerator

Start with the given expression

Break up the roots

Simplify to get . Simplify to get . Simplify to get

Multiply and combine the roots

So simplifies to

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Now let's simplify the denominator

Start with the given expression

Break up the roots

Simplify to get . Simplify to get

Multiply and combine the roots

So simplifies to

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So now our expression becomes

Divide to get

Combine the roots

Divide to get

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Answer:

So simplifies to

In other words,
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