Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

1. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{-1}{2}}}\)
2. \(\dfrac{y^{\frac{1}{3}}}{y^{-1}}\)
3. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{-5}{4}}}\)
4. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{1}{2}}}\)
5. \(\dfrac{y^{-1}}{y^{\frac{-1}{2}}}\)
6. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{3}{5}}}\)
7. \(\dfrac{a^{2}}{a^{\frac{-5}{6}}}\)
8. \(\dfrac{y^{\frac{4}{5}}}{y^{\frac{1}{6}}}\)
9. \(\dfrac{x^{-1}}{x^{-1}}\)
10. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{1}{2}}}\)
11. \(\dfrac{x^{\frac{1}{2}}}{x^{1}}\)
12. \(\dfrac{x^{\frac{5}{6}}}{x^{\frac{-3}{4}}}\)

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-2}{5} - (\frac{-1}{2}) }= x^{\frac{1}{10}}\\=\sqrt[10]{ x }\\---------------\)
2. \(\dfrac{y^{\frac{1}{3}}}{y^{-1}}\\= y^{ \frac{1}{3} - (-1) }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
3. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{-5}{4} - (\frac{-5}{4}) }= x^{0}\\=1\\---------------\)
4. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-3}{4} - \frac{1}{2} }= y^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ y^{5} }}\\=\frac{1}{|y|.\sqrt[4]{ y }}=\frac{1}{|y|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{2}|}\\---------------\)
5. \(\dfrac{y^{-1}}{y^{\frac{-1}{2}}}\\= y^{ -1 - (\frac{-1}{2}) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
6. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{3}{5}}}\\= x^{ \frac{2}{3} - \frac{3}{5} }= x^{\frac{1}{15}}\\=\sqrt[15]{ x }\\---------------\)
7. \(\dfrac{a^{2}}{a^{\frac{-5}{6}}}\\= a^{ 2 - (\frac{-5}{6}) }= a^{\frac{17}{6}}\\=\sqrt[6]{ a^{17} }=|a^{2}|.\sqrt[6]{ a^{5} }\\---------------\)
8. \(\dfrac{y^{\frac{4}{5}}}{y^{\frac{1}{6}}}\\= y^{ \frac{4}{5} - \frac{1}{6} }= y^{\frac{19}{30}}\\=\sqrt[30]{ y^{19} }\\---------------\)
9. \(\dfrac{x^{-1}}{x^{-1}}\\= x^{ -1 - (-1) }= x^{0}\\=1\\---------------\)
10. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{1}{2}}}\\= y^{ \frac{1}{2} - \frac{1}{2} }= y^{0}\\=1\\---------------\)
11. \(\dfrac{x^{\frac{1}{2}}}{x^{1}}\\= x^{ \frac{1}{2} - 1 }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
12. \(\dfrac{x^{\frac{5}{6}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{5}{6} - (\frac{-3}{4}) }= x^{\frac{19}{12}}\\=\sqrt[12]{ x^{19} }=|x|.\sqrt[12]{ x^{7} }\\---------------\)