Werk uit m.b.v. de rekenregels
- \(\dfrac{x^{-1}}{x^{\frac{3}{2}}}\)
- \(\dfrac{a^{1}}{a^{\frac{-4}{5}}}\)
- \(\dfrac{a^{-2}}{a^{\frac{1}{2}}}\)
- \(\dfrac{y^{\frac{4}{5}}}{y^{1}}\)
- \(\dfrac{x^{-1}}{x^{\frac{2}{3}}}\)
- \(\dfrac{y^{2}}{y^{\frac{2}{5}}}\)
- \(\dfrac{a^{\frac{-3}{5}}}{a^{\frac{-2}{5}}}\)
- \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{5}{6}}}\)
- \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{1}{2}}}\)
- \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{-1}{2}}}\)
- \(\dfrac{a^{-1}}{a^{\frac{4}{5}}}\)
- \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{1}{6}}}\)
Werk uit m.b.v. de rekenregels
Verbetersleutel
- \(\dfrac{x^{-1}}{x^{\frac{3}{2}}}\\= x^{ -1 - \frac{3}{2} }= x^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ x^{5} } }\\=\frac{1}{|x^{2}|. \sqrt{ x } }=\frac{1}{|x^{2}|. \sqrt{ x } }
\color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{3}|}\\---------------\)
- \(\dfrac{a^{1}}{a^{\frac{-4}{5}}}\\= a^{ 1 - (\frac{-4}{5}) }= a^{\frac{9}{5}}\\=\sqrt[5]{ a^{9} }=a.\sqrt[5]{ a^{4} }\\---------------\)
- \(\dfrac{a^{-2}}{a^{\frac{1}{2}}}\\= a^{ -2 - \frac{1}{2} }= a^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ a^{5} } }\\=\frac{1}{|a^{2}|. \sqrt{ a } }=\frac{1}{|a^{2}|. \sqrt{ a } }
\color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{3}|}\\---------------\)
- \(\dfrac{y^{\frac{4}{5}}}{y^{1}}\\= y^{ \frac{4}{5} - 1 }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}.
\color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)
- \(\dfrac{x^{-1}}{x^{\frac{2}{3}}}\\= x^{ -1 - \frac{2}{3} }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }}
\color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
- \(\dfrac{y^{2}}{y^{\frac{2}{5}}}\\= y^{ 2 - \frac{2}{5} }= y^{\frac{8}{5}}\\=\sqrt[5]{ y^{8} }=y.\sqrt[5]{ y^{3} }\\---------------\)
- \(\dfrac{a^{\frac{-3}{5}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{-3}{5} - (\frac{-2}{5}) }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}.
\color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
- \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{5}{6}}}\\= a^{ \frac{1}{2} - \frac{5}{6} }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}.
\color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
- \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-2}{5} - \frac{1}{2} }= x^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ x^{9} }}=\frac{1}{\sqrt[10]{ x^{9} }}.
\color{purple}{\frac{\sqrt[10]{ x }}{\sqrt[10]{ x }}} \\=\frac{\sqrt[10]{ x }}{|x|}\\---------------\)
- \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{5}{4} - (\frac{-1}{2}) }= x^{\frac{7}{4}}\\=\sqrt[4]{ x^{7} }=|x|.\sqrt[4]{ x^{3} }\\---------------\)
- \(\dfrac{a^{-1}}{a^{\frac{4}{5}}}\\= a^{ -1 - \frac{4}{5} }= a^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ a^{9} }}\\=\frac{1}{a.\sqrt[5]{ a^{4} }}=\frac{1}{a.\sqrt[5]{ a^{4} }}
\color{purple}{\frac{\sqrt[5]{ a }}{\sqrt[5]{ a }}} \\=\frac{\sqrt[5]{ a }}{a^{2}}\\---------------\)
- \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{1}{6}}}\\= y^{ \frac{-2}{3} - \frac{1}{6} }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}.
\color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)