How do you simplify the following expression?

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1 Answer
Mar 24, 2018

Answer:

See below for the detailed steps.

The simplified form is #4root(6)(x^11y^7)#

Explanation:

We can write a root as a fractional exponent or vice versa, so let's start here:

#(4x^3y)^(1/2)*(8xy^2)^(1/3)#

When we have an exponent on an expression in brackets we mutiply exponents:

#(4^(1/2)x^(3/2)y^(1/2))*(8^(1/3)x^(1/3)y^(2/3))#

Now #4^(1/2)=2# and #8^(1/3)=2# with that we can collect like terms by multiplying, and to multiply we add exponents:

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

#=4x^((3/2+1/3))y^((1/2+2/3))#

#=4x^((9/6+2/6))y^((3/6+4/6))#

#=4x^((11/6))y^((7/6))#

#=4root(6)(x^11y^7)#