Werk uit m.b.v. de rekenregels
- \(\dfrac{y^{\frac{-3}{5}}}{y^{-1}}\)
- \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-2}{3}}}\)
- \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{5}{3}}}\)
- \(\dfrac{q^{\frac{5}{4}}}{q^{1}}\)
- \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-1}{2}}}\)
- \(\dfrac{y^{\frac{5}{6}}}{y^{\frac{2}{3}}}\)
- \(\dfrac{y^{\frac{-1}{4}}}{y^{\frac{5}{6}}}\)
- \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{3}{5}}}\)
- \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-5}{6}}}\)
- \(\dfrac{a^{1}}{a^{\frac{-5}{2}}}\)
- \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-4}{3}}}\)
- \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{1}{5}}}\)
Werk uit m.b.v. de rekenregels
Verbetersleutel
- \(\dfrac{y^{\frac{-3}{5}}}{y^{-1}}\\= y^{ \frac{-3}{5} - (-1) }= y^{\frac{2}{5}}\\=\sqrt[5]{ y^{2} }\\---------------\)
- \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{-1}{2} - (\frac{-2}{3}) }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
- \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{5}{3}}}\\= x^{ \frac{-5}{2} - \frac{5}{3} }= x^{\frac{-25}{6}}\\=\frac{1}{\sqrt[6]{ x^{25} }}\\=\frac{1}{|x^{4}|.\sqrt[6]{ x }}=\frac{1}{|x^{4}|.\sqrt[6]{ x }}
\color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{5}|}\\---------------\)
- \(\dfrac{q^{\frac{5}{4}}}{q^{1}}\\= q^{ \frac{5}{4} - 1 }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
- \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{1}{2} - (\frac{-1}{2}) }= q^{1}\\\\---------------\)
- \(\dfrac{y^{\frac{5}{6}}}{y^{\frac{2}{3}}}\\= y^{ \frac{5}{6} - \frac{2}{3} }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
- \(\dfrac{y^{\frac{-1}{4}}}{y^{\frac{5}{6}}}\\= y^{ \frac{-1}{4} - \frac{5}{6} }= y^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ y^{13} }}\\=\frac{1}{|y|.\sqrt[12]{ y }}=\frac{1}{|y|.\sqrt[12]{ y }}
\color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y^{2}|}\\---------------\)
- \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{3}{5}}}\\= y^{ \frac{1}{3} - \frac{3}{5} }= y^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ y^{4} }}=\frac{1}{\sqrt[15]{ y^{4} }}.
\color{purple}{\frac{\sqrt[15]{ y^{11} }}{\sqrt[15]{ y^{11} }}} \\=\frac{\sqrt[15]{ y^{11} }}{y}\\---------------\)
- \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-5}{6}}}\\= q^{ \frac{-1}{2} - (\frac{-5}{6}) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
- \(\dfrac{a^{1}}{a^{\frac{-5}{2}}}\\= a^{ 1 - (\frac{-5}{2}) }= a^{\frac{7}{2}}\\= \sqrt{ a^{7} } =|a^{3}|. \sqrt{ a } \\---------------\)
- \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{-2}{3} - (\frac{-4}{3}) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
- \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{1}{5}}}\\= y^{ \frac{-1}{5} - \frac{1}{5} }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}.
\color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)