Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{5}{4}}}\\= x^{ \frac{3}{5} - \frac{5}{4} }= x^{\frac{-13}{20}}\\=\frac{1}{\sqrt[20]{ x^{13} }}=\frac{1}{\sqrt[20]{ x^{13} }}. \color{purple}{\frac{\sqrt[20]{ x^{7} }}{\sqrt[20]{ x^{7} }}} \\=\frac{\sqrt[20]{ x^{7} }}{|x|}\\---------------\)
2. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{-1}{2} - (\frac{-3}{4}) }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
3. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{-1}{2} - (\frac{-1}{3}) }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
4. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-3}{5} - (\frac{-1}{2}) }= x^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ x }}=\frac{1}{\sqrt[10]{ x }}. \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x|}\\---------------\)
5. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{1}{2}}}\\= y^{ \frac{1}{3} - \frac{1}{2} }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
6. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{3}{5}}}\\= y^{ \frac{5}{2} - \frac{3}{5} }= y^{\frac{19}{10}}\\=\sqrt[10]{ y^{19} }=|y|.\sqrt[10]{ y^{9} }\\---------------\)
7. \(\dfrac{y^{\frac{3}{2}}}{y^{\frac{-3}{2}}}\\= y^{ \frac{3}{2} - (\frac{-3}{2}) }= y^{3}\\\\---------------\)
8. \(\dfrac{a^{-1}}{a^{-2}}\\= a^{ -1 - (-2) }= a^{1}\\\\---------------\)
9. \(\dfrac{q^{\frac{5}{6}}}{q^{1}}\\= q^{ \frac{5}{6} - 1 }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
10. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{5}{3}}}\\= a^{ \frac{2}{3} - \frac{5}{3} }= a^{-1}\\=\frac{1}{a}\\---------------\)
11. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{4}{5}}}\\= q^{ \frac{-2}{3} - \frac{4}{5} }= q^{\frac{-22}{15}}\\=\frac{1}{\sqrt[15]{ q^{22} }}\\=\frac{1}{q.\sqrt[15]{ q^{7} }}=\frac{1}{q.\sqrt[15]{ q^{7} }} \color{purple}{\frac{\sqrt[15]{ q^{8} }}{\sqrt[15]{ q^{8} }}} \\=\frac{\sqrt[15]{ q^{8} }}{q^{2}}\\---------------\)
12. \(\dfrac{a^{\frac{3}{4}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{3}{4} - (\frac{-2}{3}) }= a^{\frac{17}{12}}\\=\sqrt[12]{ a^{17} }=|a|.\sqrt[12]{ a^{5} }\\---------------\)