anonymous
  • anonymous
Medal! Simplify. Your answer should contain only positive exponents with no fractional exponents in the denominator.
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[4m^\frac{ 4 }{ 3 }*m^\frac{ -7 }{ 4 }\]
Nnesha
  • Nnesha
\[\huge\rm x^m \times x^n = x^{m+n}\] exponent rule! when u multiply same bases you should ad their exponents
anonymous
  • anonymous
i don't now how to add the fractions. because they've got different denominators

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Nnesha
  • Nnesha
multiply them
Nnesha
  • Nnesha
\[\frac{ 4 }{ 3 } + \frac{ -7 }{ 4 } = \frac{ ? }{ 3(4) }\]
anonymous
  • anonymous
\[\frac{ -28 }{ 12 }\]
Nnesha
  • Nnesha
|dw:1433698357618:dw| 4 and 3 are the denominator first fraction doesn't have 4 at the denominator so multiply 4 times 4 2nd fraction -7 doesn't have 3 at the denominator so multiply it by 3 same like cross multiplication but don't forget the signs
anonymous
  • anonymous
which equals\[\frac{ 7}{ 3 }\]
anonymous
  • anonymous
wait, what?
anonymous
  • anonymous
i just realized, because they're exponents, wouldn't i be adding the fractions, not multiplying?
Nnesha
  • Nnesha
yes add \[\frac{ 4 }{ 3 } \color{Red}{+} \frac{\color{blue}{ -}7 }{ 4 } = \frac{ 4 }{3 } \color{reD}{-}\frac{7}{4}\] here positive times negative = negative now 3 and 4 both are common denominator
Nnesha
  • Nnesha
the*
Nnesha
  • Nnesha
yes add \[\frac{ 4 }{ 3 } \color{Red}{+} \frac{\color{blue}{ -}7 }{ 4 } = \frac{ 4 }{3 } \color{reD}{-}\frac{7}{4}=\frac{????}{3(4)}\] now cross multiply don't forget the negative sign |dw:1433698871386:dw|
anonymous
  • anonymous
\[\frac{ 28 }{ 12 }\]
anonymous
  • anonymous
that's what i got before but that's when you're multiplying it and they need to be added because they're exponents.
Nnesha
  • Nnesha
how did you get 28?
Nnesha
  • Nnesha
|dw:1433699227333:dw| or in other words multiply first fraction by 4 and 2nd fraction by 3
Nnesha
  • Nnesha
\[\frac{ 4 }{ 3 } \color{Red}{+} \frac{\color{blue}{ -}7 }{ 4 } = \frac{ 4 }{3 } \color{reD}{-}\frac{7}{4}= \frac{4(4) - 3(7)}{3(4)}\] like this
anonymous
  • anonymous
\[\frac{ 16-21 }{ 12 }\]
anonymous
  • anonymous
\[\frac{ -5 }{ 12 }\]
anonymous
  • anonymous
like that?
Nnesha
  • Nnesha
yes that's right so \[\large\rm 4m^\frac{ 4 }{ 3 }*m^\frac{ -7 }{ 4 } = ???\]
anonymous
  • anonymous
\[4m^\frac{ -5 }{ 12 }\]
Nnesha
  • Nnesha
yep right now there is another exponent rules \[\huge\rm x^{-m} = \frac{ 1 }{ x^m }\]
anonymous
  • anonymous
yup. got that. thank you!
Nnesha
  • Nnesha
np :-)

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