Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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