Werk uit m.b.v. de rekenregels
- \(\dfrac{q^{\frac{3}{2}}}{q^{\frac{3}{4}}}\)
- \(\dfrac{q^{\frac{-5}{2}}}{q^{1}}\)
- \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-1}{3}}}\)
- \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{1}{2}}}\)
- \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-1}{5}}}\)
- \(\dfrac{y^{\frac{1}{2}}}{y^{1}}\)
- \(\dfrac{y^{\frac{-2}{3}}}{y^{1}}\)
- \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{1}{3}}}\)
- \(\dfrac{x^{\frac{-5}{2}}}{x^{-1}}\)
- \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-2}{5}}}\)
- \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{-3}{5}}}\)
- \(\dfrac{q^{2}}{q^{\frac{-1}{6}}}\)
Werk uit m.b.v. de rekenregels
Verbetersleutel
- \(\dfrac{q^{\frac{3}{2}}}{q^{\frac{3}{4}}}\\= q^{ \frac{3}{2} - \frac{3}{4} }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
- \(\dfrac{q^{\frac{-5}{2}}}{q^{1}}\\= q^{ \frac{-5}{2} - 1 }= q^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ q^{7} } }\\=\frac{1}{|q^{3}|. \sqrt{ q } }=\frac{1}{|q^{3}|. \sqrt{ q } }
\color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{4}|}\\---------------\)
- \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-1}{2} - (\frac{-1}{3}) }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}.
\color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
- \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-1}{2} - \frac{1}{2} }= y^{-1}\\=\frac{1}{y}\\---------------\)
- \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-1}{5}}}\\= a^{ \frac{-2}{3} - (\frac{-1}{5}) }= a^{\frac{-7}{15}}\\=\frac{1}{\sqrt[15]{ a^{7} }}=\frac{1}{\sqrt[15]{ a^{7} }}.
\color{purple}{\frac{\sqrt[15]{ a^{8} }}{\sqrt[15]{ a^{8} }}} \\=\frac{\sqrt[15]{ a^{8} }}{a}\\---------------\)
- \(\dfrac{y^{\frac{1}{2}}}{y^{1}}\\= y^{ \frac{1}{2} - 1 }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }.
\color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
- \(\dfrac{y^{\frac{-2}{3}}}{y^{1}}\\= y^{ \frac{-2}{3} - 1 }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }}
\color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
- \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{1}{3}}}\\= a^{ \frac{3}{5} - \frac{1}{3} }= a^{\frac{4}{15}}\\=\sqrt[15]{ a^{4} }\\---------------\)
- \(\dfrac{x^{\frac{-5}{2}}}{x^{-1}}\\= x^{ \frac{-5}{2} - (-1) }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } }
\color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
- \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{-1}{2} - (\frac{-2}{5}) }= y^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ y }}=\frac{1}{\sqrt[10]{ y }}.
\color{purple}{\frac{\sqrt[10]{ y^{9} }}{\sqrt[10]{ y^{9} }}} \\=\frac{\sqrt[10]{ y^{9} }}{|y|}\\---------------\)
- \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{1}{4} - (\frac{-3}{5}) }= y^{\frac{17}{20}}\\=\sqrt[20]{ y^{17} }\\---------------\)
- \(\dfrac{q^{2}}{q^{\frac{-1}{6}}}\\= q^{ 2 - (\frac{-1}{6}) }= q^{\frac{13}{6}}\\=\sqrt[6]{ q^{13} }=|q^{2}|.\sqrt[6]{ q }\\---------------\)