How do you simplify #(3x^-2y^2)/(6xy^2)#?

Answer 1

#1/(2x^3)#

Using the #color(blue)"laws of exponents"#
#color(orange)"Reminder"#
#color(red)(|bar(ul(color(white)(a/a)color(black)(a^nxxa^m=a^(n+m)" and " a^-mhArr1/a^m)color(white)(a/a)|)))#
#rArr(3x^-2y^2)/(6xy^2)" can be expressed as"#
#3/6xxx^-2/x xxy^2/y^2#
#=cancel(3)^1/(cancel(6)^2)xx1/x^(1+2)xx(cancel(y^2)^1)/cancel(y2)^1#
#=1/2xx1/x^3xx1=(1xx1xx1)/(2xxx^3xx1)=1/(2x^3)#
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Answer 2

To simplify ( \frac{3x^{-2}y^2}{6xy^2} ), follow these steps:

  1. Combine the constants: ( \frac{3}{6} = \frac{1}{2} ).
  2. Combine the variables with the same base by subtracting their exponents: ( x^{-2} ) in the numerator and ( x^1 ) in the denominator, resulting in ( x^{-2-1} = x^{-3} ).
  3. Combine the variables ( y^2 ) in the numerator and ( y^2 ) in the denominator, resulting in ( y^{2-2} = y^0 = 1 ).
  4. The simplified expression is ( \frac{1}{2x^3} ).
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Answer 3

To simplify (\frac{3x^{-2}y^2}{6xy^2}), first combine like terms in the numerator and denominator. Then, simplify the expression by canceling out common factors between the numerator and denominator.

[ \frac{3x^{-2}y^2}{6xy^2} = \frac{3}{6} \cdot \frac{x^{-2}y^2}{xy^2} = \frac{1}{2} \cdot \frac{x^{-2}}{x} = \frac{1}{2} \cdot x^{-2-1} = \frac{1}{2}x^{-3} = \frac{1}{2x^3} ]

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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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