Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{-1}}{y^{\frac{-4}{3}}}\\= y^{ -1 - (\frac{-4}{3}) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
2. \(\dfrac{y^{1}}{y^{\frac{-1}{2}}}\\= y^{ 1 - (\frac{-1}{2}) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
3. \(\dfrac{y^{-1}}{y^{1}}\\= y^{ -1 - 1 }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
4. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-1}{3} - \frac{1}{3} }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
5. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{-5}{4} - (\frac{-3}{5}) }= x^{\frac{-13}{20}}\\=\frac{1}{\sqrt[20]{ x^{13} }}=\frac{1}{\sqrt[20]{ x^{13} }}. \color{purple}{\frac{\sqrt[20]{ x^{7} }}{\sqrt[20]{ x^{7} }}} \\=\frac{\sqrt[20]{ x^{7} }}{|x|}\\---------------\)
6. \(\dfrac{y^{\frac{5}{6}}}{y^{\frac{3}{5}}}\\= y^{ \frac{5}{6} - \frac{3}{5} }= y^{\frac{7}{30}}\\=\sqrt[30]{ y^{7} }\\---------------\)
7. \(\dfrac{a^{\frac{5}{2}}}{a^{-1}}\\= a^{ \frac{5}{2} - (-1) }= a^{\frac{7}{2}}\\= \sqrt{ a^{7} } =|a^{3}|. \sqrt{ a } \\---------------\)
8. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{-5}{4} - (\frac{-4}{3}) }= x^{\frac{1}{12}}\\=\sqrt[12]{ x }\\---------------\)
9. \(\dfrac{x^{\frac{2}{3}}}{x^{1}}\\= x^{ \frac{2}{3} - 1 }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
10. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-3}{4} - \frac{1}{3} }= a^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ a^{13} }}\\=\frac{1}{|a|.\sqrt[12]{ a }}=\frac{1}{|a|.\sqrt[12]{ a }} \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a^{2}|}\\---------------\)
11. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-5}{4}}}\\= y^{ \frac{1}{2} - (\frac{-5}{4}) }= y^{\frac{7}{4}}\\=\sqrt[4]{ y^{7} }=|y|.\sqrt[4]{ y^{3} }\\---------------\)
12. \(\dfrac{a^{\frac{-4}{3}}}{a^{\frac{-5}{3}}}\\= a^{ \frac{-4}{3} - (\frac{-5}{3}) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)