Question

Simplify the expression below.

14a^8y^3-7a^4y^5+28a^12y^2/7a^4y

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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`