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solniwko [45]
3 years ago
7

uestion 4 of 10structions: Select the correct answer from the drop down menu.(xy)nsider the expressione equivalent simplified fo

rm of this expression isx 3/9/(xn-7)ext Reset

Mathematics
2 answers:
nata0808 [166]3 years ago
7 0
\dfrac{(xy)^{-2}}{(3y)^2x^{-5}}=\dfrac{x^{-2}y^{-2}}{9y^2x^{-5}}=\dfrac{x^3}{9y^4}
nadya68 [22]3 years ago
3 0

Answer:

\frac{x^{3} }{9y^{4} }

Step-by-step explanation:

The given expression is

\frac{(xy)^{-2} }{(3y)^{2} x^{-5} }

First, we use the property: (xy)^{2} =x^{2} y^{2}

\frac{(xy)^{-2} }{(3y)^{2} x^{-5} }=\frac{x^{-2} y^{-2} }{9y^{2} x^{-5} }

Then, we use the property: \frac{x^{m} }{x^{n} }=x^{m-n}

\frac{x^{-2} y^{-2} }{9y^{2} x^{-5} }=\frac{x^{-2+5} y^{-2-2} }{9} =\frac{x^{3}y^{-4}  }{9}

Next, we use the property: x^{-n} =\frac{1}{x^{-n} }

\frac{x^{3}y^{-4}  }{9}=\frac{x^{3} }{9y^{4} }

Therefore, the answer is

\frac{x^{3} }{9y^{4} }

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Step-by-step explanation:

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3 years ago
If x>2, then x^2-x-6/x^2-4=
Viefleur [7K]
Consider the expression \frac{x^{2} -x-6}{ x^{2} -4}

To factorize the expression in the denominator we use difference of squares: x^{2} -4=x^{2} - 2^{2} =(x-2)(x+2)

To factorize x^{2} -x-6 we use the following method:

x^{2} -x-6=(x-a)(x-b)

where a, b are 2 numbers such that a+b= -1, the coefficient of x,

and a*b= -6, the constant.

such 2 numbers can be easily checked to be -3 and 2

(-3*2=6, -3+2=-1)

So x^{2} -x-6=(x-a)(x-b)=(x+3)(x-2)


 \frac{x^{2} -x-6}{ x^{2} -4}= \frac{(x+3)(x-2)}{(x-2)(x+2)}= \frac{x+3}{x+2}


\frac{x+3}{x+2}= \frac{x+2+1}{x+2}= \frac{x+2}{x+2}+ \frac{1}{x+2}=1+ \frac{1}{x+2}

for x>2

\frac{1}{x+2}\ \textless \  \frac{1}{2+2}= \frac{1}{4}

thus

for x>2, 

1+ \frac{1}{x+2}\ \textless \ 1+ \frac{1}{4}= \frac{5}{4}


Answer: 

for x>2

\frac{x^{2} -x-6}{ x^{2} -4} =  \frac{x+3}{x+2} \ \textless \  \frac{5}{4}, (but the expression is never 0)
8 0
4 years ago
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