Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{3}{2}}}{y^{-1}}\\= y^{ \frac{3}{2} - (-1) }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)
2. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{4}{5}}}\\= y^{ \frac{2}{3} - \frac{4}{5} }= y^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ y^{2} }}=\frac{1}{\sqrt[15]{ y^{2} }}. \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y}\\---------------\)
3. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{5}{3}}}\\= q^{ \frac{2}{5} - \frac{5}{3} }= q^{\frac{-19}{15}}\\=\frac{1}{\sqrt[15]{ q^{19} }}\\=\frac{1}{q.\sqrt[15]{ q^{4} }}=\frac{1}{q.\sqrt[15]{ q^{4} }} \color{purple}{\frac{\sqrt[15]{ q^{11} }}{\sqrt[15]{ q^{11} }}} \\=\frac{\sqrt[15]{ q^{11} }}{q^{2}}\\---------------\)
4. \(\dfrac{y^{\frac{-5}{3}}}{y^{-1}}\\= y^{ \frac{-5}{3} - (-1) }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
5. \(\dfrac{y^{\frac{-1}{3}}}{y^{1}}\\= y^{ \frac{-1}{3} - 1 }= y^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ y^{4} }}\\=\frac{1}{y.\sqrt[3]{ y }}=\frac{1}{y.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{2}}\\---------------\)
6. \(\dfrac{a^{1}}{a^{\frac{-2}{3}}}\\= a^{ 1 - (\frac{-2}{3}) }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
7. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{-1}{2} - (\frac{-2}{3}) }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
8. \(\dfrac{a^{-1}}{a^{\frac{-1}{4}}}\\= a^{ -1 - (\frac{-1}{4}) }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
9. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{1}{3} - (\frac{-1}{3}) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
10. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{4}{3} - (\frac{-1}{6}) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
11. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{2}{5}}}\\= q^{ \frac{2}{3} - \frac{2}{5} }= q^{\frac{4}{15}}\\=\sqrt[15]{ q^{4} }\\---------------\)
12. \(\dfrac{x^{\frac{1}{5}}}{x^{\frac{-3}{2}}}\\= x^{ \frac{1}{5} - (\frac{-3}{2}) }= x^{\frac{17}{10}}\\=\sqrt[10]{ x^{17} }=|x|.\sqrt[10]{ x^{7} }\\---------------\)