Question

Plz help quick How do you do this problem

Answer 1

Answer: $\frac{pr}{675}$

Step-by-step explanation:

1. cant have a negative exponent
2. $\frac{1}{(3p^{-1} r)^3(5pr^{-2} )^2}$
3. split up (3p^-1 r)^3
4. rewrite that part of the equation
5. $\frac{1}{(\frac{3}{p} )^{3} r^{3} }$
6. raise 3 to the power of 3 = 27
7. p to the power of 3 = $p^{3}$
8. Next part of the equation
9. $(5p)^{2}$
10. expand that
11. $5^{2} p^{2}$
12. simplfy
13. $25p^{2}$
14. Next part of the equation
15. $(r^{-2})^{2}$
16. multiply the exponents
17. $r^{-4}$
18. rewrite the equation
19. $\frac{1}{\frac{27}{p^{3} }r^{3} (25p^{2})\frac{1}{r^{4} } }$
20. combine $\frac{27}{p^{3} } , and , r^{3}$  = $\frac{27r^{3} }{p^{3} }$
21. combine 25 and $\frac{27r^{3} }{p^{3} }$
22. Multiply
23. $\frac{675r^{3} }{p^{3} }$
24. combine $\frac{675r^{3} }{p^{3} }$ and $p^{2}$
25. $\frac{675r^{3}p^{2} }{p^{3} }$
26. multiply $\frac{675r^{3}p^{2} }{p^{3} }$ and $\frac{1}{r^{4} }$
27. $\frac{1}{\frac{675r^{3}p^{2} }{p^{3}r^{4} }}$
28. cancel the common factors and factor everything out
29. $r^{3}$ comes out of ${675r^{3}p^{2} }$  
30. $r^{3}$ can also come out of $p^{3} r^{4}$
31. Rewrite as $\frac{1}{\frac{675p^{2} }{p^{3} r} }$
32. cancel the common factor of $p^{2}$ and $p^{3}$
33. factor $p^{2}$ out of $675p^{2}$ by mulitiplying
34.  factor $p^{2}$ out of ${p^{3} r} }$
35. cancel the common factor
36. rewrite the expression
37. $\frac{1}{\frac{675}{pr} }$
38. and then multiply the numerator and denominator
39. and you get the answer