Simplify the following expression.

Question

StartFraction 4 x Superscript negative 2 Baseline y Superscript 4 Over 12 x cubed left parenthesis y Superscript negative 2 Baseline right parenthesis cubed EndFraction
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Part 1
StartFraction 4 x Superscript negative 2 Baseline y Superscript 4 Over 12 x cubed left parenthesis y Superscript negative 2 Baseline right parenthesis cubed EndFraction
equals
  
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​(Use positive exponents​ only.)

Answer 1

To simplify the expression, we can apply the properties of exponents:

First, let's simplify the numerator:
4x^(-2)y^4 = 4/y^2

Now, let's simplify the denominator:
12x^3(y^(-2))^3 = 12x^3/y^6

Therefore, the simplified expression is:
(4/y^2) / (12x^3/y^6)

To divide fractions, we can multiply by the reciprocal of the second fraction:
(4/y^2) * (y^6/12x^3) = (4y^6) / (12x^3 * y^2)
= (4y^6) / (12x^3y^2)

Now, let's simplify further by canceling out common factors:
= (1/3) * (y^6 / x^3y^2)
= (1/3) * (y^4 / x^3) [cancelling out y^2]

Therefore, the simplified expression is (1/3) * (y^4 / x^3).