Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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