Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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