Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{3}{4}}}{a^{\frac{-4}{3}}}\\= a^{ \frac{3}{4} - (\frac{-4}{3}) }= a^{\frac{25}{12}}\\=\sqrt[12]{ a^{25} }=|a^{2}|.\sqrt[12]{ a }\\---------------\)
2. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{4}{3}}}\\= q^{ \frac{-1}{3} - \frac{4}{3} }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
3. \(\dfrac{x^{\frac{2}{5}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{2}{5} - (\frac{-2}{3}) }= x^{\frac{16}{15}}\\=\sqrt[15]{ x^{16} }=x.\sqrt[15]{ x }\\---------------\)
4. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{2}{5}}}\\= x^{ \frac{-1}{2} - \frac{2}{5} }= x^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ x^{9} }}=\frac{1}{\sqrt[10]{ x^{9} }}. \color{purple}{\frac{\sqrt[10]{ x }}{\sqrt[10]{ x }}} \\=\frac{\sqrt[10]{ x }}{|x|}\\---------------\)
5. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{5}{3}}}\\= q^{ \frac{-1}{3} - \frac{5}{3} }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
6. \(\dfrac{a^{\frac{-1}{5}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-1}{5} - (\frac{-1}{3}) }= a^{\frac{2}{15}}\\=\sqrt[15]{ a^{2} }\\---------------\)
7. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{1}{2} - (\frac{-3}{5}) }= x^{\frac{11}{10}}\\=\sqrt[10]{ x^{11} }=|x|.\sqrt[10]{ x }\\---------------\)
8. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{3}{2}}}\\= y^{ \frac{2}{3} - \frac{3}{2} }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
9. \(\dfrac{y^{-1}}{y^{-1}}\\= y^{ -1 - (-1) }= y^{0}\\=1\\---------------\)
10. \(\dfrac{a^{\frac{-4}{5}}}{a^{-1}}\\= a^{ \frac{-4}{5} - (-1) }= a^{\frac{1}{5}}\\=\sqrt[5]{ a }\\---------------\)
11. \(\dfrac{a^{\frac{5}{4}}}{a^{\frac{1}{5}}}\\= a^{ \frac{5}{4} - \frac{1}{5} }= a^{\frac{21}{20}}\\=\sqrt[20]{ a^{21} }=|a|.\sqrt[20]{ a }\\---------------\)
12. \(\dfrac{a^{\frac{4}{3}}}{a^{\frac{2}{5}}}\\= a^{ \frac{4}{3} - \frac{2}{5} }= a^{\frac{14}{15}}\\=\sqrt[15]{ a^{14} }\\---------------\)