anonymous
  • anonymous
square root problem
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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cathyangs
  • cathyangs
which is?
anonymous
  • anonymous
the expression \[\sqrt[4]{16x ^{2}y ^{7}?}\] is equivalent to which? 2x^(1/2)y^(7/4) , 4x^(1/2)y^(7/4), 2x^8y^28, or 4x^8y^28.
anonymous
  • anonymous
sorry it took me so long

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anonymous
  • anonymous
Use the the fundamental rule with radicals that (ab)^(1/2) = (a)^(1/2) * (b)^(1/2)
anonymous
  • anonymous
Do you understand radicals? They are simply used to determine what two (or 4 in this case) identical numbers multiply together to give what is under the radical for example 3^(2) = 9 3*3 = 9 (9)^(1/2) =3
anonymous
  • anonymous
i know but how does that help me find what the equation is equivalent to?
anonymous
  • anonymous
so split up the terms of your problem into (16)^(1/4) * (x^(2))^(1/4) * (y^(7))^(1/4) I will solve the first term to show you how to solve this so we have (16)^(1/4) if you raise 2^(4) you realize you can get 16 so it simplifies to just 2 so now you are left with 2 * (x^(2))^(1/4) * (y^(7))^(1/4) Now to solve a variable what times what give y^(7) that will allow it to be simplified (when multiplying numbers with exponents we add the exponents). so we have 2 * (x^(2))^(1/4) * (y^(4))^(1/4) * (y^(3))^(1/4)
anonymous
  • anonymous
do you know what the next step is?
anonymous
  • anonymous
??
anonymous
  • anonymous
remember the rule that (x^(4))^(1/4) is the same as x^((x/1)(1/4)) = x^(1) = x
anonymous
  • anonymous
um do i i change (x^2)^1/4 into x?
anonymous
  • anonymous
wait apply the rule I just showed you so (x^(2))^(1/4) = x^((2/1)(1/4))
anonymous
  • anonymous
you know how to multiply fractions right and that all numbers can be expressed with a 1 in the denominator
anonymous
  • anonymous
and how to simplify fractions right? (2/4) = (1/2)
anonymous
  • anonymous
ya so um it turns out to be x^1/2?
anonymous
  • anonymous
yup
anonymous
  • anonymous
what is (y^(3))^(1/4) simplified?
anonymous
  • anonymous
2x^1/2 and y^7/4
anonymous
  • anonymous
y^(7/4) can be simplified more you would know that if you read what I posted
anonymous
  • anonymous
you can split up numbers and variables to aid in simplification of them
anonymous
  • anonymous
ya but that is what it looks like as one of the answer choices
anonymous
  • anonymous
oh ok weird sorry for the accusation hope I was helpful
anonymous
  • anonymous
ya u were ty

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