How do you rewrite this expression in simplest radical form: #(4x^3y^4)^(3/2)#?

1 Answer
Ben
Mar 23, 2018

The simplified version is #8y^6x^4 sqrt(x)#

Explanation:

When you take an exponent of an exponent, it's equal to multiplying both exponents together. Using this tip, we can distribute the #3/2# exponent as follows:

NOTE: When I color something #color(red)("red")# it means it's in the simplest form.

#(4x^3y^4)^(3/2)=4^(3/2)xx x^(3*3/2)xx y^(4*3/2)#

#=4^(3/2)xx x^(9/2)xx y^(12/2)#

#=4^(3/2)xx x^(9/2)xx color(red)(y^6)#

Next, lets simplify the first two terms:

#4^(3/2)=(4^(1/2))^3=(sqrt(4))^3 = 2^3=color(red)(8)#

#x^(9/2)=x^(4 1/2)=color(red)(x^4 sqrt(x))#

Finally, let's reassemble:

#(4x^3y^4)^(3/2)=color(red)(8y^6 x^4 sqrt(x))#

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