Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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