How do you simplify #root4(x^12/y^4)#?

Answer 1

#root4(x^12/y^4) = x^3/y#

#root4(x^12/y^4) = (x^12/y^4)^(1/4) =(x^12 * y^-4)^(1/4)#
Remember the rule of indices: #(a^m)^n = a^(m xx n)#

Applying this rule to the expression:

#(x^12 * y^-4)^(1/4) = x^(12/4) * y^(-4/4)#
#= x^3 * y^-1#
#= x^3/y#
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Answer 2

Detailed explanation:

#color(blue)(root(4)((x^12)/(y^4))#

Let's solve it using simple steps

First we should know that #color(brown)(root(x)(y/z)=(root(x)(y))/(root(x)(z))#

So,

#rarrroot(4)((x^12)/(y^4))=(root(4)(x^12))/(root(4)(y^4))#
Now solve #root(4)(x^12)# and #root(4)(y^4)# each independantly
Let's solve #root(4)(x^12)# (expand it)
#rarrroot(4)(x^12)=root(4)(x*x*x*x*x*x*x*x*x*x*x*x)#

Take out the roots

#rarrroot(4)(underbrace(x*x*x*x)*underbrace(x*x*x*x)*underbrace(x*x*x*x))#
#rarrx*x*x#
#color(green)(rArrx^3#
Now solve #root(4)(y^4)# (expand it)
#rarrroot(4)(y^4)=root(4)(y*y*y*y)#

Take out the roots

#rarrroot(4)(underbrace(y*y*y*y))#
#color(green)(rArry#

So, put the solutions together to get our answer

#color(blue)(x^3/y#

Hope this helps! :)

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Answer 3

To simplify ( \sqrt[4]{\frac{x^{12}}{y^4}} ), you can rewrite it as ( \frac{x^{12/4}}{y^{4/4}} ), which simplifies to ( \frac{x^3}{y} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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