Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{1}}{x^{\frac{1}{5}}}\\= x^{ 1 - \frac{1}{5} }= x^{\frac{4}{5}}\\=\sqrt[5]{ x^{4} }\\---------------\)
2. \(\dfrac{y^{-1}}{y^{\frac{5}{3}}}\\= y^{ -1 - \frac{5}{3} }= y^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ y^{8} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }}=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{3}}\\---------------\)
3. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{-1}{6}}}\\= x^{ \frac{-2}{3} - (\frac{-1}{6}) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
4. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{1}{3}}}\\= x^{ \frac{3}{5} - \frac{1}{3} }= x^{\frac{4}{15}}\\=\sqrt[15]{ x^{4} }\\---------------\)
5. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-4}{3} - \frac{1}{3} }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
6. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{-1}{5} - (\frac{-2}{3}) }= y^{\frac{7}{15}}\\=\sqrt[15]{ y^{7} }\\---------------\)
7. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{-2}{3} - (\frac{-5}{6}) }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
8. \(\dfrac{y^{1}}{y^{\frac{-1}{3}}}\\= y^{ 1 - (\frac{-1}{3}) }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
9. \(\dfrac{a^{\frac{-1}{5}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-1}{5} - \frac{2}{3} }= a^{\frac{-13}{15}}\\=\frac{1}{\sqrt[15]{ a^{13} }}=\frac{1}{\sqrt[15]{ a^{13} }}. \color{purple}{\frac{\sqrt[15]{ a^{2} }}{\sqrt[15]{ a^{2} }}} \\=\frac{\sqrt[15]{ a^{2} }}{a}\\---------------\)
10. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{1}{4}}}\\= q^{ \frac{5}{3} - \frac{1}{4} }= q^{\frac{17}{12}}\\=\sqrt[12]{ q^{17} }=|q|.\sqrt[12]{ q^{5} }\\---------------\)
11. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{3}{5}}}\\= a^{ \frac{-3}{4} - \frac{3}{5} }= a^{\frac{-27}{20}}\\=\frac{1}{\sqrt[20]{ a^{27} }}\\=\frac{1}{|a|.\sqrt[20]{ a^{7} }}=\frac{1}{|a|.\sqrt[20]{ a^{7} }} \color{purple}{\frac{\sqrt[20]{ a^{13} }}{\sqrt[20]{ a^{13} }}} \\=\frac{\sqrt[20]{ a^{13} }}{|a^{2}|}\\---------------\)
12. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{4}{3}}}\\= a^{ \frac{1}{2} - \frac{4}{3} }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)