Question

Simplify the expression below.

Answer 1

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

$\bf \cfrac{14a^8y^3-7a^4y^5+28a^{12}y^2}{7a^4y}\impliedby \begin{array}{llll} \textit{let us first, distribute}\\ the~denominator \end{array} \\\\\\ \cfrac{14a^8y^3}{7a^4y}-\cfrac{7a^4y^5}{7a^4y}+\cfrac{28a^{12}y^2}{7a^4y} \\\\\\ \cfrac{14}{7}a^8a^{-4}y^{-1} y^3-\cfrac{7}{7}a^4a^{-4}y^{-1} y^5+\cfrac{28}{7}a^{12}a^{-4}y^{-1} y^2 \\\\\\ 2a^{8-4}y^{-1+3}-1a^{4-4}y^{-1+5}+4a^{12-4}y^{-1+2} \\\\\\ 2a^4y^2-1\cdot 1y^4+4a^8y\implies 2a^4y^2-y^4+4a^8y$