rationalize the denominator: 17x over the fourth root of 9x to the 7th power y to the sixth poweralgebra

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shaznl1 | High School Teacher | (Level 1) Salutatorian

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if your question means 17x/ (4sqrt(9x))^7*y^6), then the procedures will be as follows

times on top and bottom 4sqrt(729x^3)

the fraction becomes

(17x*4sqrt(729x^3))/(4 sqrt(9x*729*x^3)*y^6)

Then the inside of the 4th root becomes 6561 x^4, and the fourth root is just 9 x

put that into the fraction

it becomes (17x*4sqrt(729x^3))/(9x*y^6)

the x cancels on the top side and bottom

it becomes


If you mean the y^6 is not on the bottom, then just leave it aside and multiply it later

 this question uses that the fourth power of something could cancel out the fourth root, so the fourth power of 9x is 6561x^4 and we had 9x already in the 4th root, so we need to time 729x^3 to the 4th root so that there would be no more radicals on the bottom of the equation, making it rationalized