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Could someone explain this with work?

20 points (: Could someone explain this with work?-example-1

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notice that, if you move a factor from the bottom to above, you'd change its sign, and if you move it from above to the bottom, you also have to change its sign, thus,


\bf \left.\qquad \qquad \right.\textit{negative exponents}\\\\ a^{-{ n}} \implies \cfrac{1}{a^( n)} \qquad \qquad \cfrac{1}{a^( n)}\implies a^{-{ n}} \qquad \qquad a^{{{ n}}}\implies \cfrac{1}{a^{-{{ n}}}} \\\\ -------------------------------\\\\


\bf \cfrac{3(4x^4y^3)^2}{(5x^2y^6)^3}\impliedby \textit{first off, we distribute the exponent} \\\\\\ \cfrac{3(4^2x^(4\cdot 2)y^(3\cdot 2))}{5^3x^(2\cdot 3)y^(6\cdot 3)}\implies \cfrac{3(16x^8y^6)}{125x^6y^(18)}\implies \cfrac{48x^8y^6}{125x^6y^(18)}\implies \cfrac{48x^8x^(-6)}{125y^(18)y^(-6)} \\\\\\ \cfrac{48x^(8-6)}{125y^(18-6)}\implies \cfrac{48x^2}{125y^(12)}
User Arsen Davtyan
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