Question

20 points (:
Could someone explain this with work?

Answer 1

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)}`