Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{3}{5} - (\frac{-1}{3}) }= x^{\frac{14}{15}}\\=\sqrt[15]{ x^{14} }\\---------------\)
2. \(\dfrac{x^{\frac{2}{5}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{2}{5} - (\frac{-1}{2}) }= x^{\frac{9}{10}}\\=\sqrt[10]{ x^{9} }\\---------------\)
3. \(\dfrac{a^{\frac{5}{4}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{5}{4} - (\frac{-2}{5}) }= a^{\frac{33}{20}}\\=\sqrt[20]{ a^{33} }=|a|.\sqrt[20]{ a^{13} }\\---------------\)
4. \(\dfrac{q^{-1}}{q^{\frac{4}{3}}}\\= q^{ -1 - \frac{4}{3} }= q^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ q^{7} }}\\=\frac{1}{q^{2}.\sqrt[3]{ q }}=\frac{1}{q^{2}.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{3}}\\---------------\)
5. \(\dfrac{a^{\frac{-4}{5}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-4}{5} - (\frac{-1}{3}) }= a^{\frac{-7}{15}}\\=\frac{1}{\sqrt[15]{ a^{7} }}=\frac{1}{\sqrt[15]{ a^{7} }}. \color{purple}{\frac{\sqrt[15]{ a^{8} }}{\sqrt[15]{ a^{8} }}} \\=\frac{\sqrt[15]{ a^{8} }}{a}\\---------------\)
6. \(\dfrac{q^{\frac{3}{5}}}{q^{\frac{5}{2}}}\\= q^{ \frac{3}{5} - \frac{5}{2} }= q^{\frac{-19}{10}}\\=\frac{1}{\sqrt[10]{ q^{19} }}\\=\frac{1}{|q|.\sqrt[10]{ q^{9} }}=\frac{1}{|q|.\sqrt[10]{ q^{9} }} \color{purple}{\frac{\sqrt[10]{ q }}{\sqrt[10]{ q }}} \\=\frac{\sqrt[10]{ q }}{|q^{2}|}\\---------------\)
7. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-5}{3}}}\\= y^{ \frac{1}{2} - (\frac{-5}{3}) }= y^{\frac{13}{6}}\\=\sqrt[6]{ y^{13} }=|y^{2}|.\sqrt[6]{ y }\\---------------\)
8. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{-1}{6} - (\frac{-5}{2}) }= q^{\frac{7}{3}}\\=\sqrt[3]{ q^{7} }=q^{2}.\sqrt[3]{ q }\\---------------\)
9. \(\dfrac{q^{\frac{-5}{3}}}{q^{\frac{1}{5}}}\\= q^{ \frac{-5}{3} - \frac{1}{5} }= q^{\frac{-28}{15}}\\=\frac{1}{\sqrt[15]{ q^{28} }}\\=\frac{1}{q.\sqrt[15]{ q^{13} }}=\frac{1}{q.\sqrt[15]{ q^{13} }} \color{purple}{\frac{\sqrt[15]{ q^{2} }}{\sqrt[15]{ q^{2} }}} \\=\frac{\sqrt[15]{ q^{2} }}{q^{2}}\\---------------\)
10. \(\dfrac{a^{\frac{-4}{3}}}{a^{\frac{2}{5}}}\\= a^{ \frac{-4}{3} - \frac{2}{5} }= a^{\frac{-26}{15}}\\=\frac{1}{\sqrt[15]{ a^{26} }}\\=\frac{1}{a.\sqrt[15]{ a^{11} }}=\frac{1}{a.\sqrt[15]{ a^{11} }} \color{purple}{\frac{\sqrt[15]{ a^{4} }}{\sqrt[15]{ a^{4} }}} \\=\frac{\sqrt[15]{ a^{4} }}{a^{2}}\\---------------\)
11. \(\dfrac{a^{\frac{-3}{5}}}{a^{\frac{5}{2}}}\\= a^{ \frac{-3}{5} - \frac{5}{2} }= a^{\frac{-31}{10}}\\=\frac{1}{\sqrt[10]{ a^{31} }}\\=\frac{1}{|a^{3}|.\sqrt[10]{ a }}=\frac{1}{|a^{3}|.\sqrt[10]{ a }} \color{purple}{\frac{\sqrt[10]{ a^{9} }}{\sqrt[10]{ a^{9} }}} \\=\frac{\sqrt[10]{ a^{9} }}{|a^{4}|}\\---------------\)
12. \(\dfrac{y^{1}}{y^{\frac{1}{3}}}\\= y^{ 1 - \frac{1}{3} }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)