DF001
  • DF001
help with 7x^3y(3x^-1y^5/9x^3y^-2)^-3
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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DF001
  • DF001
\[7x ^{3}y(\frac{ 3x ^{-1} y^5 }{ 9x ^{3}y ^{-2} })^{-3}\]
DF001
  • DF001
I am stuck on this question and I need help before an hour for class
mathstudent55
  • mathstudent55
Is this the problem? \(\large 7x^3y \left( \dfrac{3x^{-1}y^5}{9x^3y^-2} \right) ^{-3}\)

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More answers

DF001
  • DF001
|dw:1441208422555:dw|
DF001
  • DF001
yes and i am stuck on this process
DF001
  • DF001
The answer is 189x^9/y^20 but, i want to know how it is done
mathstudent55
  • mathstudent55
We can start by simplifying the fraction inside the parentheses. Keep the exponent -3 as it is. We are first just working inside the parentheses.
DF001
  • DF001
How can I simplify the inside
mathstudent55
  • mathstudent55
\(\large 7x^3y \left( \dfrac{3x^{-1}y^5}{9x^3y^-2} \right) ^{-3}\) \(\large =7x^3y \left( \dfrac{y^7}{3x^4} \right) ^{-3}\)
mathstudent55
  • mathstudent55
A negative exponent in the denominator is a positive exponent in the numerator. A negative exponent in the numerator is a positive exponent in the denominator.
mathstudent55
  • mathstudent55
Ok so far?
DF001
  • DF001
wait, where did the 9 go
mathstudent55
  • mathstudent55
The 3 and the nine get reduced to 1/3. Now we deal with the negative exponent, -3. We make the exponent positive by flipping the fraction.
mathstudent55
  • mathstudent55
\(\large = 7x^3y \left( \dfrac{3x^4}{y^7} \right) ^{3}\)
mathstudent55
  • mathstudent55
|dw:1441208660696:dw|
mathstudent55
  • mathstudent55
|dw:1441208697400:dw|
DF001
  • DF001
oh you only flip the numbers in front?
mathstudent55
  • mathstudent55
When you flipped the fraction, you forgot to flip the 9 and the 3. Yes, you do flip the numbers because the numbers are also part of the numerator and denominator.
DF001
  • DF001
do I leave the variables alone
mathstudent55
  • mathstudent55
After flipping, you can reduce the 9 and the 3 to 3 and 1, or just 3 in the numerator.
mathstudent55
  • mathstudent55
Notice that your corrected figure (with the 3 and 1) are exactly what I am up to in Latex above.
DF001
  • DF001
|dw:1441209037907:dw|
mathstudent55
  • mathstudent55
Now we raise the fraction to the 3rd power. To raise a fraction to a power, raise the numerator and the denominator to the power.
mathstudent55
  • mathstudent55
\(\large = 7x^3y \cdot \dfrac{(3x^4)^3}{(y^7)^3} \) Ok?
dinamix
  • dinamix
and he should find it 189 *(x^15/y^20) @mathstudent55
mathstudent55
  • mathstudent55
Now we raise the numerator and denominator to the 3rd power by raising every factor. \(\large = 7x^3y\cdot \dfrac{3^3(x^4)^3}{y^{21}} \) \(\large = 7x^3y\cdot \dfrac{27x^{12}}{y^{21}} \) \(\large = \dfrac{7x^3y\cdot 27x^{12}}{y^{21}} \) \(\large = \dfrac{189x^{15}}{y^{20}} \)
mathstudent55
  • mathstudent55
|dw:1441209750213:dw|
mathstudent55
  • mathstudent55
|dw:1441209770713:dw|

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