Question

Factor and simplify the algebraic expression.

3x^-4/3 +6x^1/3

Thanks in advance if you can help me!

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}}}} \\\\\\ and\qquad a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^( n)} \qquad \qquad \sqrt[{ m}]{a^( n)}\implies a^{\frac{{ n}}{{ m}}}\\\\ -------------------------------\\\\`


`\fb 3x^{-(4)/(3)}+6x^{(1)/(3)}\implies 3\cdot \cfrac{1}{x^{(4)/(3)}}+6x^{(1)/(3)}\implies \cfrac{3}{x^{(4)/(3)}}+6x^{(1)/(3)}\impliedby LCD=x^{(4)/(3)} \\\\\\ \cfrac{3+(6x^{(1)/(3)})(x^{(4)/(3)})}{x^{(4)/(3)}}\implies \cfrac{3+6x^{(1)/(3)+(4)/(3)}}{x^{(4)/(3)}}\implies \cfrac{3+6x^{(5)/(3)}}{x^{(4)/(3)}}\implies \cfrac{3+6\sqrt[3]{x^5}}{\sqrt[3]{x^4}}`

that'd be hmmm a kinda simplification of it, not sure if I could call it a simplified version, more like an expansion though.