Simplify (the answer shouldn't have any negative exponents)

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Simplify (the answer shouldn't have any negative exponents)

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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\[\left( \frac{ 3 }{ 2 } \frac{ x ^{-12}x ^{8}y ^{10} }{ x ^{5}y ^{4}y ^{-7} }\right)^{-3}\]
If we apply the rules of multiplication and division of power with same basis, we get: \[\Large {\left( {\frac{3}{2}{x^{ - 12 + 8 - 5}}{y^{10 - 4 - \left( { - 7} \right)}}} \right)^{ - 3}}\]
please simplify

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First, focus on the exponents. then we apply one of the laws of exponents, which generally has the form: \(\huge (\frac{p^n}{q^m})^r = \frac{p^{n+r}}{q^{n+r}}\)
CAN you perform the indicated operation for the exponent portion in your problem?
@nincompoop no, I don't know much about exponential equations
\(\color{blue}{\text{Originally Posted by}}\) @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 \[\huge\rm (\frac{ p^n }{ p^m })^r = \frac{ p^{nr} }{ q^{mr} }\] ??
so do I multiply all of the exponents and the 3/2 in the parentheses by -3?
(i meant give 3/2 an exponent of -3)
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 \[\huge\rm { x^{-m} }={ \frac{ 1 }{ x^m } }\]
\(\color{blue}{\text{Originally Posted by}}\) @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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