clara1223
  • clara1223
Simplify (the answer shouldn't have any negative exponents)
Mathematics
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SOLVED
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katieb
  • katieb
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clara1223
  • clara1223
\[\left( \frac{ 3 }{ 2 } \frac{ x ^{-12}x ^{8}y ^{10} }{ x ^{5}y ^{4}y ^{-7} }\right)^{-3}\]
Michele_Laino
  • Michele_Laino
If we apply the rules of multiplication and division of power with same basis, we get: \[\Large {\left( {\frac{3}{2}{x^{ - 12 + 8 - 5}}{y^{10 - 4 - \left( { - 7} \right)}}} \right)^{ - 3}}\]
Michele_Laino
  • Michele_Laino
please simplify

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nincompoop
  • nincompoop
First, focus on the exponents. then we apply one of the laws of exponents, which generally has the form: \(\huge (\frac{p^n}{q^m})^r = \frac{p^{n+r}}{q^{n+r}}\)
nincompoop
  • nincompoop
CAN you perform the indicated operation for the exponent portion in your problem?
clara1223
  • clara1223
@nincompoop no, I don't know much about exponential equations
Nnesha
  • Nnesha
\(\color{blue}{\text{Originally Posted by}}\) @nincompoop First, focus on the exponents. then we apply one of the laws of exponents, which generally has the form: \(\huge (\frac{p^n}{q^m})^r = \frac{p^{n+r}}{q^{n+r}}\) \(\color{blue}{\text{End of Quote}}\) n+r or n times r mhm i guess you meant \[\huge\rm (\frac{ p^n }{ p^m })^r = \frac{ p^{nr} }{ q^{mr} }\] ??
clara1223
  • clara1223
so do I multiply all of the exponents and the 3/2 in the parentheses by -3?
clara1223
  • clara1223
(i meant give 3/2 an exponent of -3)
Nnesha
  • Nnesha
when you multiply same bases then you should add their expnents you need to know exponent rules first one is \[\huge\rm \frac{ x^m }{ x^n } = x^{m-n}\] if there are same bases at the numerator and at the denominator move exponent frm bottom to top or top to bottom(remember there shouldn't be any negative exponent) 2nd rule \[\huge\rm (\frac{ x^m }{ y^n })^r = \frac{ x^{m \times r} }{ y^{n \times r}}\] 3rd one is \[\huge\rm { x^{-m} }={ \frac{ 1 }{ x^m } }\]
Nnesha
  • Nnesha
\(\color{blue}{\text{Originally Posted by}}\) @clara1223 (i meant give 3/2 an exponent of -3) \(\color{blue}{\text{End of Quote}}\) yep \[(\frac{ 3 }{ 2 })^{-3}\]

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