Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{1}{2} - (\frac{-4}{3}) }= q^{\frac{11}{6}}\\=\sqrt[6]{ q^{11} }=|q|.\sqrt[6]{ q^{5} }\\---------------\)
2. \(\dfrac{a^{\frac{3}{2}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{3}{2} - (\frac{-1}{2}) }= a^{2}\\\\---------------\)
3. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{5}{3} - (\frac{-1}{2}) }= q^{\frac{13}{6}}\\=\sqrt[6]{ q^{13} }=|q^{2}|.\sqrt[6]{ q }\\---------------\)
4. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{2}{3}}}\\= x^{ \frac{5}{4} - \frac{2}{3} }= x^{\frac{7}{12}}\\=\sqrt[12]{ x^{7} }\\---------------\)
5. \(\dfrac{y^{1}}{y^{\frac{1}{4}}}\\= y^{ 1 - \frac{1}{4} }= y^{\frac{3}{4}}\\=\sqrt[4]{ y^{3} }\\---------------\)
6. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{4}{5} - (\frac{-2}{3}) }= a^{\frac{22}{15}}\\=\sqrt[15]{ a^{22} }=a.\sqrt[15]{ a^{7} }\\---------------\)
7. \(\dfrac{x^{\frac{1}{6}}}{x^{\frac{2}{3}}}\\= x^{ \frac{1}{6} - \frac{2}{3} }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
8. \(\dfrac{q^{\frac{4}{5}}}{q^{\frac{2}{3}}}\\= q^{ \frac{4}{5} - \frac{2}{3} }= q^{\frac{2}{15}}\\=\sqrt[15]{ q^{2} }\\---------------\)
9. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{-1}{4}}}\\= a^{ \frac{3}{5} - (\frac{-1}{4}) }= a^{\frac{17}{20}}\\=\sqrt[20]{ a^{17} }\\---------------\)
10. \(\dfrac{y^{1}}{y^{-1}}\\= y^{ 1 - (-1) }= y^{2}\\\\---------------\)
11. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-1}{2} - (\frac{-1}{3}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
12. \(\dfrac{x^{\frac{-2}{3}}}{x^{2}}\\= x^{ \frac{-2}{3} - 2 }= x^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ x^{8} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x^{2} }}=\frac{1}{x^{2}.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{3}}\\---------------\)