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Sagot :
Answer: [tex]\frac{pr}{675}[/tex]
Step-by-step explanation:
- cant have a negative exponent
- [tex]\frac{1}{(3p^{-1} r)^3(5pr^{-2} )^2} \\[/tex]
- split up (3p^-1 r)^3
- rewrite that part of the equation
- [tex]\frac{1}{(\frac{3}{p} )^{3} r^{3} }[/tex]
- raise 3 to the power of 3 = 27
- p to the power of 3 = [tex]p^{3}[/tex]
- Next part of the equation
- [tex](5p)^{2}[/tex]
- expand that
- [tex]5^{2} p^{2}[/tex]
- simplfy
- [tex]25p^{2}[/tex]
- Next part of the equation
- [tex](r^{-2})^{2}[/tex]
- multiply the exponents
- [tex]r^{-4}[/tex]
- rewrite the equation
- [tex]\frac{1}{\frac{27}{p^{3} }r^{3} (25p^{2})\frac{1}{r^{4} } }[/tex]
- combine [tex]\frac{27}{p^{3} } , and , r^{3}[/tex] = [tex]\frac{27r^{3} }{p^{3} }[/tex]
- combine 25 and [tex]\frac{27r^{3} }{p^{3} }[/tex]
- Multiply
- [tex]\frac{675r^{3} }{p^{3} }[/tex]
- combine [tex]\frac{675r^{3} }{p^{3} }[/tex] and [tex]p^{2}[/tex]
- [tex]\frac{675r^{3}p^{2} }{p^{3} }[/tex]
- multiply [tex]\frac{675r^{3}p^{2} }{p^{3} }[/tex] and [tex]\frac{1}{r^{4} }[/tex]
- [tex]\frac{1}{\frac{675r^{3}p^{2} }{p^{3}r^{4} }}[/tex]
- cancel the common factors and factor everything out
- [tex]r^{3}[/tex] comes out of [tex]{675r^{3}p^{2} }[/tex]
- [tex]r^{3}[/tex] can also come out of [tex]p^{3} r^{4}[/tex]
- Rewrite as [tex]\frac{1}{\frac{675p^{2} }{p^{3} r} }[/tex]
- cancel the common factor of [tex]p^{2}[/tex] and [tex]p^{3}[/tex]
- factor [tex]p^{2}[/tex] out of [tex]675p^{2}[/tex] by mulitiplying
- factor [tex]p^{2}[/tex] out of [tex]{p^{3} r} }[/tex]
- cancel the common factor
- rewrite the expression
- [tex]\frac{1}{\frac{675}{pr} }[/tex]
- and then multiply the numerator and denominator
- and you get the answer
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