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Marina86 [1]
3 years ago
11

Plz help quick How do you do this problem

Mathematics
1 answer:
astraxan [27]3 years ago
7 0

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  
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