Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{1}{3}}}\\= q^{ \frac{1}{3} - \frac{1}{3} }= q^{0}\\=1\\---------------\)
2. \(\dfrac{q^{\frac{4}{3}}}{q^{2}}\\= q^{ \frac{4}{3} - 2 }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
3. \(\dfrac{a^{\frac{-4}{3}}}{a^{1}}\\= a^{ \frac{-4}{3} - 1 }= a^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ a^{7} }}\\=\frac{1}{a^{2}.\sqrt[3]{ a }}=\frac{1}{a^{2}.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{3}}\\---------------\)
4. \(\dfrac{q^{\frac{3}{2}}}{q^{\frac{1}{3}}}\\= q^{ \frac{3}{2} - \frac{1}{3} }= q^{\frac{7}{6}}\\=\sqrt[6]{ q^{7} }=|q|.\sqrt[6]{ q }\\---------------\)
5. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-1}{5}}}\\= a^{ \frac{2}{3} - (\frac{-1}{5}) }= a^{\frac{13}{15}}\\=\sqrt[15]{ a^{13} }\\---------------\)
6. \(\dfrac{x^{\frac{5}{2}}}{x^{1}}\\= x^{ \frac{5}{2} - 1 }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
7. \(\dfrac{a^{\frac{1}{2}}}{a^{-1}}\\= a^{ \frac{1}{2} - (-1) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
8. \(\dfrac{y^{-1}}{y^{\frac{1}{3}}}\\= y^{ -1 - \frac{1}{3} }= y^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ y^{4} }}\\=\frac{1}{y.\sqrt[3]{ y }}=\frac{1}{y.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{2}}\\---------------\)
9. \(\dfrac{x^{1}}{x^{\frac{-1}{6}}}\\= x^{ 1 - (\frac{-1}{6}) }= x^{\frac{7}{6}}\\=\sqrt[6]{ x^{7} }=|x|.\sqrt[6]{ x }\\---------------\)
10. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{-3}{2}}}\\= x^{ \frac{-2}{3} - (\frac{-3}{2}) }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
11. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{5}{2}}}\\= q^{ \frac{5}{6} - \frac{5}{2} }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
12. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-1}{3} - (\frac{-1}{2}) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)