How to Simplify a Complicated Equation?

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The discussion centers on simplifying the equation (\frac{ab^2c^{-3}}{2a^3b^{-4}})^{-2}. The correct simplification results in \frac{4a^4c^{6}}{b^{12}}. Key rules highlighted include flipping the fraction for negative exponents and applying the exponent to each part of a product. For those unsure of their calculations, using a calculator is suggested as a reliable alternative. The conversation emphasizes understanding the rules of exponents for accurate simplification.
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is this right??

Hello

I am simplifying this right?



(\frac{ab^2c^{-3}}{2a^3b^{-4}})^{-2}


\frac{4a^4c^{6}}{b^{12}}


Thanks
P
 
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Yes you have.
 
just remember the simple rules: if its a negative exponent flip the fraction, and if you have a product under the exponent each part is raised to the power separately.

ofcourse you can always just plug it into a calculator if you don't trust yourself at all...
 
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