How do you simplify #-3x^2y^3zsqrt(75x^9y^4z^10)#?

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Answer 1 · 2015-06-01T01:49:56

Remembering one exponential law which states that #a^(n/m)=root(m)(a^n)#, we can rewrite the function as

#-3x^2y^3z75^(1/2)x^(9/2)y^(4/2)z^(10/2)#

(As this is a square root, we have that, for the exponential rule, #m=2#)

Now, following another law of exponentials, we have that #a^n*a^m=a^(n+m)#

#-3x^((2+9/2))y^((3+2))z^((1+10/2))75^(1/2)#

#-3x^(13/2)y^5z^(6)75^(1/2)#

We can rewrite the element #75^(1/2)# as #(3*25)^(1/2)=3^(1/2)*25^(1/2)#

Thus, we can combine the first #-3# with the just-factored #3#:

#-(3)^(1)*(3^(1/2))x^(13/2)y^5z^(6)75^(1/2)25^(1/2)#

As #25^(1/2)=sqrt(25)=5#,

#5(-3)^(1.5)x^(6.5)y^5z^(6)#