Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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