How do you simplify #\root [ 3] { \frac{ 8x ^ { 3} }{ y ^ { 6} } }#?

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Answer 1 · 2017-01-02T02:45:08

You need to use various rules of exponents to simplify this expression. See the full explanation below.

#root(3)((8x^3)/y^6)# can be rewritten as:

#((8x^3)/y^6)^(1/3)#

One rule for exponents is:

#color(red)((x^a)^b = x^(a*b))#

Applying this rule to the expression for this problem yields:

#(8^(1/3)x^(3*1/3))/y^(6*1/3) = #

#(8^(1/3)x^1)/y^2#

Another rule of exponents is:

#color(red)(x^1 = x)#

Using this gives:

#(8^(1/3)x)/y^2 = #

#(2x)/y^2#