What is #((x^8)/y^4)^(3/4)#?

1 Answer
NickTheTurtle
Apr 4, 2017

#x^6/y^3#

Explanation:

Remember that #(a/b)^c=a^c/b^c#. We can use this property to simplify the expression #(x^8/y^4)^(3/4)=((x^8)^(3/4))/((y^4)^(3/4))#.

Now, we use another property of powers: #(a^b)^c=a^(bc)#. We can apply this property to both the numerator and the denominator: #((x^8)^(3/4))/((y^4)^(3/4))=x^(8*3/4)/y^(4*3/4)=x^6/y^3#.

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