Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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