Werk uit m.b.v. de rekenregels
- \(\dfrac{a^{\frac{5}{4}}}{a^{\frac{5}{4}}}\)
- \(\dfrac{a^{\frac{-2}{5}}}{a^{\frac{1}{2}}}\)
- \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-1}{6}}}\)
- \(\dfrac{a^{-2}}{a^{\frac{-2}{3}}}\)
- \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-1}{6}}}\)
- \(\dfrac{q^{\frac{-1}{3}}}{q^{1}}\)
- \(\dfrac{a^{\frac{-1}{5}}}{a^{-1}}\)
- \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{-1}{6}}}\)
- \(\dfrac{q^{\frac{3}{2}}}{q^{\frac{5}{2}}}\)
- \(\dfrac{a^{\frac{-5}{2}}}{a^{1}}\)
- \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{1}{4}}}\)
- \(\dfrac{y^{-2}}{y^{\frac{3}{4}}}\)
Werk uit m.b.v. de rekenregels
Verbetersleutel
- \(\dfrac{a^{\frac{5}{4}}}{a^{\frac{5}{4}}}\\= a^{ \frac{5}{4} - \frac{5}{4} }= a^{0}\\=1\\---------------\)
- \(\dfrac{a^{\frac{-2}{5}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-2}{5} - \frac{1}{2} }= a^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ a^{9} }}=\frac{1}{\sqrt[10]{ a^{9} }}.
\color{purple}{\frac{\sqrt[10]{ a }}{\sqrt[10]{ a }}} \\=\frac{\sqrt[10]{ a }}{|a|}\\---------------\)
- \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{-2}{3} - (\frac{-1}{6}) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }.
\color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
- \(\dfrac{a^{-2}}{a^{\frac{-2}{3}}}\\= a^{ -2 - (\frac{-2}{3}) }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }}
\color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
- \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-1}{6}}}\\= x^{ \frac{-1}{3} - (\frac{-1}{6}) }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}.
\color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
- \(\dfrac{q^{\frac{-1}{3}}}{q^{1}}\\= q^{ \frac{-1}{3} - 1 }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }}
\color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
- \(\dfrac{a^{\frac{-1}{5}}}{a^{-1}}\\= a^{ \frac{-1}{5} - (-1) }= a^{\frac{4}{5}}\\=\sqrt[5]{ a^{4} }\\---------------\)
- \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{1}{3} - (\frac{-1}{6}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
- \(\dfrac{q^{\frac{3}{2}}}{q^{\frac{5}{2}}}\\= q^{ \frac{3}{2} - \frac{5}{2} }= q^{-1}\\=\frac{1}{q}\\---------------\)
- \(\dfrac{a^{\frac{-5}{2}}}{a^{1}}\\= a^{ \frac{-5}{2} - 1 }= a^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ a^{7} } }\\=\frac{1}{|a^{3}|. \sqrt{ a } }=\frac{1}{|a^{3}|. \sqrt{ a } }
\color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{4}|}\\---------------\)
- \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{1}{4}}}\\= y^{ \frac{1}{2} - \frac{1}{4} }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
- \(\dfrac{y^{-2}}{y^{\frac{3}{4}}}\\= y^{ -2 - \frac{3}{4} }= y^{\frac{-11}{4}}\\=\frac{1}{\sqrt[4]{ y^{11} }}\\=\frac{1}{|y^{2}|.\sqrt[4]{ y^{3} }}=\frac{1}{|y^{2}|.\sqrt[4]{ y^{3} }}
\color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y^{3}|}\\---------------\)