SOLUTION: {{cube root of 108x^3y^7/2y^3}}

Question 203101This question is from textbook
: {{cube root of 108x^3y^7/2y^3}} This question is from textbook

Found 2 solutions by jim_thompson5910, jsmallt9:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given expression.

Reduce the coefficients.

Divide the common variable terms by subtracting the exponents.

Subtract

Factor 54 into 27*2

Factor into

Break up the root.

Take the cube root of 27 to get 3

Take the cube root of to get "x"

Take the cube root of to get "y"

Rearrange the terms and combine the roots.

So where
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

Let's start by reducing the fraction inside:

Now we look for perfect cube factors:

Now we can use one of the properties of roots (which apply for all roots: square, cube, 4th, 5th, etc.): . This allows us to separate factors in a root into separate roots:

Now we can simplify the cube roots of the perfect cubes:

Using the Commutative Property of multiplication to rearrange the order:

And finally, using the same property of roots as earlier (except in reverse), to combine the cube roots:

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