Werk uit m.b.v. de rekenregels
- \(\dfrac{x^{\frac{5}{6}}}{x^{\frac{-2}{3}}}\)
- \(\dfrac{q^{\frac{-2}{5}}}{q^{\frac{5}{2}}}\)
- \(\dfrac{a^{1}}{a^{\frac{-1}{2}}}\)
- \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{-1}{3}}}\)
- \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{1}{2}}}\)
- \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{-1}{2}}}\)
- \(\dfrac{q^{-1}}{q^{-1}}\)
- \(\dfrac{y^{\frac{-5}{4}}}{y^{-1}}\)
- \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{5}{6}}}\)
- \(\dfrac{y^{\frac{-1}{4}}}{y^{\frac{-2}{3}}}\)
- \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{1}{5}}}\)
- \(\dfrac{y^{\frac{-2}{3}}}{y^{-2}}\)
Werk uit m.b.v. de rekenregels
Verbetersleutel
- \(\dfrac{x^{\frac{5}{6}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{5}{6} - (\frac{-2}{3}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
- \(\dfrac{q^{\frac{-2}{5}}}{q^{\frac{5}{2}}}\\= q^{ \frac{-2}{5} - \frac{5}{2} }= q^{\frac{-29}{10}}\\=\frac{1}{\sqrt[10]{ q^{29} }}\\=\frac{1}{|q^{2}|.\sqrt[10]{ q^{9} }}=\frac{1}{|q^{2}|.\sqrt[10]{ q^{9} }}
\color{purple}{\frac{\sqrt[10]{ q }}{\sqrt[10]{ q }}} \\=\frac{\sqrt[10]{ q }}{|q^{3}|}\\---------------\)
- \(\dfrac{a^{1}}{a^{\frac{-1}{2}}}\\= a^{ 1 - (\frac{-1}{2}) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
- \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{-5}{2} - (\frac{-1}{3}) }= x^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ x^{13} }}\\=\frac{1}{|x^{2}|.\sqrt[6]{ x }}=\frac{1}{|x^{2}|.\sqrt[6]{ x }}
\color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{3}|}\\---------------\)
- \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-5}{2} - \frac{1}{2} }= x^{-3}\\=\frac{1}{x^{3}}\\---------------\)
- \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{1}{3} - (\frac{-1}{2}) }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
- \(\dfrac{q^{-1}}{q^{-1}}\\= q^{ -1 - (-1) }= q^{0}\\=1\\---------------\)
- \(\dfrac{y^{\frac{-5}{4}}}{y^{-1}}\\= y^{ \frac{-5}{4} - (-1) }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}.
\color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
- \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{5}{6}}}\\= a^{ \frac{-1}{4} - \frac{5}{6} }= a^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ a^{13} }}\\=\frac{1}{|a|.\sqrt[12]{ a }}=\frac{1}{|a|.\sqrt[12]{ a }}
\color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a^{2}|}\\---------------\)
- \(\dfrac{y^{\frac{-1}{4}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{-1}{4} - (\frac{-2}{3}) }= y^{\frac{5}{12}}\\=\sqrt[12]{ y^{5} }\\---------------\)
- \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{1}{5}}}\\= x^{ \frac{3}{4} - \frac{1}{5} }= x^{\frac{11}{20}}\\=\sqrt[20]{ x^{11} }\\---------------\)
- \(\dfrac{y^{\frac{-2}{3}}}{y^{-2}}\\= y^{ \frac{-2}{3} - (-2) }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)