Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-5}{4}}}{a^{\frac{5}{3}}}\\= a^{ \frac{-5}{4} - \frac{5}{3} }= a^{\frac{-35}{12}}\\=\frac{1}{\sqrt[12]{ a^{35} }}\\=\frac{1}{|a^{2}|.\sqrt[12]{ a^{11} }}=\frac{1}{|a^{2}|.\sqrt[12]{ a^{11} }} \color{purple}{\frac{\sqrt[12]{ a }}{\sqrt[12]{ a }}} \\=\frac{\sqrt[12]{ a }}{|a^{3}|}\\---------------\)
2. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{-1}{5} - (\frac{-1}{3}) }= y^{\frac{2}{15}}\\=\sqrt[15]{ y^{2} }\\---------------\)
3. \(\dfrac{q^{\frac{4}{5}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{4}{5} - (\frac{-1}{2}) }= q^{\frac{13}{10}}\\=\sqrt[10]{ q^{13} }=|q|.\sqrt[10]{ q^{3} }\\---------------\)
4. \(\dfrac{x^{\frac{1}{3}}}{x^{-2}}\\= x^{ \frac{1}{3} - (-2) }= x^{\frac{7}{3}}\\=\sqrt[3]{ x^{7} }=x^{2}.\sqrt[3]{ x }\\---------------\)
5. \(\dfrac{a^{1}}{a^{\frac{-1}{2}}}\\= a^{ 1 - (\frac{-1}{2}) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
6. \(\dfrac{a^{-1}}{a^{-1}}\\= a^{ -1 - (-1) }= a^{0}\\=1\\---------------\)
7. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{2}{3}}}\\= q^{ \frac{1}{3} - \frac{2}{3} }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
8. \(\dfrac{y^{\frac{4}{5}}}{y^{\frac{5}{3}}}\\= y^{ \frac{4}{5} - \frac{5}{3} }= y^{\frac{-13}{15}}\\=\frac{1}{\sqrt[15]{ y^{13} }}=\frac{1}{\sqrt[15]{ y^{13} }}. \color{purple}{\frac{\sqrt[15]{ y^{2} }}{\sqrt[15]{ y^{2} }}} \\=\frac{\sqrt[15]{ y^{2} }}{y}\\---------------\)
9. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{5}{2}}}\\= a^{ \frac{-1}{3} - \frac{5}{2} }= a^{\frac{-17}{6}}\\=\frac{1}{\sqrt[6]{ a^{17} }}\\=\frac{1}{|a^{2}|.\sqrt[6]{ a^{5} }}=\frac{1}{|a^{2}|.\sqrt[6]{ a^{5} }} \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a^{3}|}\\---------------\)
10. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{1}{2} - (\frac{-2}{3}) }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)
11. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{1}{4} - (\frac{-2}{5}) }= a^{\frac{13}{20}}\\=\sqrt[20]{ a^{13} }\\---------------\)
12. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{4}{3}}}\\= x^{ \frac{1}{2} - \frac{4}{3} }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)