## DF001 one year ago help with 7x^3y(3x^-1y^5/9x^3y^-2)^-3

1. DF001

$7x ^{3}y(\frac{ 3x ^{-1} y^5 }{ 9x ^{3}y ^{-2} })^{-3}$

2. DF001

I am stuck on this question and I need help before an hour for class

3. mathstudent55

Is this the problem? $$\large 7x^3y \left( \dfrac{3x^{-1}y^5}{9x^3y^-2} \right) ^{-3}$$

4. DF001

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5. DF001

yes and i am stuck on this process

6. DF001

The answer is 189x^9/y^20 but, i want to know how it is done

7. 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.

8. DF001

How can I simplify the inside

9. mathstudent55

$$\large 7x^3y \left( \dfrac{3x^{-1}y^5}{9x^3y^-2} \right) ^{-3}$$ $$\large =7x^3y \left( \dfrac{y^7}{3x^4} \right) ^{-3}$$

10. 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.

11. mathstudent55

Ok so far?

12. DF001

wait, where did the 9 go

13. 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.

14. mathstudent55

$$\large = 7x^3y \left( \dfrac{3x^4}{y^7} \right) ^{3}$$

15. mathstudent55

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16. mathstudent55

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17. DF001

oh you only flip the numbers in front?

18. 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.

19. DF001

do I leave the variables alone

20. mathstudent55

After flipping, you can reduce the 9 and the 3 to 3 and 1, or just 3 in the numerator.

21. mathstudent55

Notice that your corrected figure (with the 3 and 1) are exactly what I am up to in Latex above.

22. DF001

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23. 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.

24. mathstudent55

$$\large = 7x^3y \cdot \dfrac{(3x^4)^3}{(y^7)^3}$$ Ok?

25. dinamix

and he should find it 189 *(x^15/y^20) @mathstudent55

26. mathstudent55

Now we raise the numerator and denominator to the 3rd power by raising every factor. $$\large = 7x^3y\cdot \dfrac{3^3(x^4)^3}{y^{21}}$$ $$\large = 7x^3y\cdot \dfrac{27x^{12}}{y^{21}}$$ $$\large = \dfrac{7x^3y\cdot 27x^{12}}{y^{21}}$$ $$\large = \dfrac{189x^{15}}{y^{20}}$$

27. mathstudent55

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28. mathstudent55

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