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ceceliasteenburgh

Answer: [tex]\frac{pr}{675}[/tex]

Step-by-step explanation:

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

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