# Calculus/Algebra/Solutions

1. Simplify the expression ${\displaystyle 144^{\frac {5}{3}}}$
${\displaystyle 144^{\frac {5}{3}}=(2^{4}\cdot 3^{2})^{\frac {5}{3}}=2^{\frac {20}{3}}\cdot 3^{\frac {10}{3}}=2^{6}{\sqrt[{3}]{2^{2}}}\cdot 3^{3}{\sqrt[{3}]{3}}=1728{\sqrt[{3}]{12}}}$
${\displaystyle 144^{\frac {5}{3}}=(2^{4}\cdot 3^{2})^{\frac {5}{3}}=2^{\frac {20}{3}}\cdot 3^{\frac {10}{3}}=2^{6}{\sqrt[{3}]{2^{2}}}\cdot 3^{3}{\sqrt[{3}]{3}}=1728{\sqrt[{3}]{12}}}$
2. Factor ${\displaystyle x-1}$ out of ${\displaystyle 6x^{3}-4x^{2}+3x-5}$.
:${\displaystyle {\begin{array}{rl}&~~\,6x^{2}+2x+5\\x-1\!\!\!\!&{\big )}\!\!\!{\begin{array}{lll}\hline \,6x^{3}-4x^{2}+3x-5\end{array}}\\&\!\!\!\!-{\underline {(6x^{3}-6x^{2})~~~}}\\&\!\!\!\!~~~~~~~~~~~~2x^{2}+3x-5~~~\\&\!\!\!\!~~~~~~~~-{\underline {(2x^{2}-2x)~~~}}\\&\!\!\!\!~~~~~~~~~~~~~~~~~~~~~5x-5~~~\\&\!\!\!\!~~~~~~~~~~~~~~~~-{\underline {(5x-5)~~~}}\\&\!\!\!\!~~~~~~~~~~~~~~~~~~~~~~~~~~~~0~~~\\\end{array}}}$ ${\displaystyle \mathbf {6x^{3}-4x^{2}+3x-5=(x-1)(6x^{2}+2x+5)} }$
:${\displaystyle {\begin{array}{rl}&~~\,6x^{2}+2x+5\\x-1\!\!\!\!&{\big )}\!\!\!{\begin{array}{lll}\hline \,6x^{3}-4x^{2}+3x-5\end{array}}\\&\!\!\!\!-{\underline {(6x^{3}-6x^{2})~~~}}\\&\!\!\!\!~~~~~~~~~~~~2x^{2}+3x-5~~~\\&\!\!\!\!~~~~~~~~-{\underline {(2x^{2}-2x)~~~}}\\&\!\!\!\!~~~~~~~~~~~~~~~~~~~~~5x-5~~~\\&\!\!\!\!~~~~~~~~~~~~~~~~-{\underline {(5x-5)~~~}}\\&\!\!\!\!~~~~~~~~~~~~~~~~~~~~~~~~~~~~0~~~\\\end{array}}}$ ${\displaystyle \mathbf {6x^{3}-4x^{2}+3x-5=(x-1)(6x^{2}+2x+5)} }$