Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{1}{4} - (\frac{-3}{5}) }= a^{\frac{17}{20}}\\=\sqrt[20]{ a^{17} }\\---------------\)
2. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-3}{4}}}\\= q^{ \frac{-1}{2} - (\frac{-3}{4}) }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
3. \(\dfrac{a^{\frac{-3}{5}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{-3}{5} - (\frac{-2}{3}) }= a^{\frac{1}{15}}\\=\sqrt[15]{ a }\\---------------\)
4. \(\dfrac{a^{\frac{3}{4}}}{a^{\frac{-4}{3}}}\\= a^{ \frac{3}{4} - (\frac{-4}{3}) }= a^{\frac{25}{12}}\\=\sqrt[12]{ a^{25} }=|a^{2}|.\sqrt[12]{ a }\\---------------\)
5. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{2}{3}}}\\= a^{ \frac{4}{5} - \frac{2}{3} }= a^{\frac{2}{15}}\\=\sqrt[15]{ a^{2} }\\---------------\)
6. \(\dfrac{x^{-1}}{x^{\frac{-2}{3}}}\\= x^{ -1 - (\frac{-2}{3}) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
7. \(\dfrac{a^{2}}{a^{2}}\\= a^{ 2 - 2 }= a^{0}\\=1\\---------------\)
8. \(\dfrac{x^{-1}}{x^{1}}\\= x^{ -1 - 1 }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
9. \(\dfrac{x^{-1}}{x^{\frac{-1}{2}}}\\= x^{ -1 - (\frac{-1}{2}) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
10. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{1}{2}}}\\= q^{ \frac{1}{4} - \frac{1}{2} }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
11. \(\dfrac{y^{-2}}{y^{\frac{-2}{3}}}\\= y^{ -2 - (\frac{-2}{3}) }= y^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ y^{4} }}\\=\frac{1}{y.\sqrt[3]{ y }}=\frac{1}{y.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{2}}\\---------------\)
12. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{4}{5}}}\\= q^{ \frac{4}{3} - \frac{4}{5} }= q^{\frac{8}{15}}\\=\sqrt[15]{ q^{8} }\\---------------\)