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I need help on this question I’m trying to understand it more better answer 14

I need help on this question I’m trying to understand it more better answer 14-example-1

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Given the expression:


((16x^(1/6)y^(-2))/(x^(-1/6)y^6))^(3/2)

We use the following property of exponents:


(z^a)/(z^b)=z^(a-b)

Then:


(16x^(1/6+1/6)y^(-2-6))^(3/2)=(4^2x^(1/3)y^(-8))^(3/2)

Now, we use the following property of exponents:


(z^a)^b=z^(a\cdot b)

Finally:


4^(2\cdot3/2)x^(1/3\cdot3/2)y^(-8\cdot3/2)=4^3x^(1/2)y^(-12)=(64x^(1/2))/(y^(12))

Answer: Option D

User Tanis
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