Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-1}{5}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{-1}{5} - (\frac{-3}{5}) }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
2. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{1}{2} - (\frac{-5}{4}) }= a^{\frac{7}{4}}\\=\sqrt[4]{ a^{7} }=|a|.\sqrt[4]{ a^{3} }\\---------------\)
3. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{-5}{3}}}\\= x^{ \frac{3}{2} - (\frac{-5}{3}) }= x^{\frac{19}{6}}\\=\sqrt[6]{ x^{19} }=|x^{3}|.\sqrt[6]{ x }\\---------------\)
4. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{5}{3}}}\\= a^{ \frac{1}{3} - \frac{5}{3} }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
5. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{2}{3} - (\frac{-4}{3}) }= y^{2}\\\\---------------\)
6. \(\dfrac{y^{1}}{y^{\frac{1}{5}}}\\= y^{ 1 - \frac{1}{5} }= y^{\frac{4}{5}}\\=\sqrt[5]{ y^{4} }\\---------------\)
7. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{5}{4}}}\\= q^{ \frac{-1}{3} - \frac{5}{4} }= q^{\frac{-19}{12}}\\=\frac{1}{\sqrt[12]{ q^{19} }}\\=\frac{1}{|q|.\sqrt[12]{ q^{7} }}=\frac{1}{|q|.\sqrt[12]{ q^{7} }} \color{purple}{\frac{\sqrt[12]{ q^{5} }}{\sqrt[12]{ q^{5} }}} \\=\frac{\sqrt[12]{ q^{5} }}{|q^{2}|}\\---------------\)
8. \(\dfrac{q^{\frac{4}{5}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{4}{5} - (\frac{-2}{3}) }= q^{\frac{22}{15}}\\=\sqrt[15]{ q^{22} }=q.\sqrt[15]{ q^{7} }\\---------------\)
9. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-2}{3} - \frac{1}{2} }= x^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[6]{ x }}=\frac{1}{|x|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{2}|}\\---------------\)
10. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{4}{5}}}\\= x^{ \frac{2}{3} - \frac{4}{5} }= x^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ x^{2} }}=\frac{1}{\sqrt[15]{ x^{2} }}. \color{purple}{\frac{\sqrt[15]{ x^{13} }}{\sqrt[15]{ x^{13} }}} \\=\frac{\sqrt[15]{ x^{13} }}{x}\\---------------\)
11. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-5}{4}}}\\= q^{ \frac{-1}{3} - (\frac{-5}{4}) }= q^{\frac{11}{12}}\\=\sqrt[12]{ q^{11} }\\---------------\)
12. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{2}{3}}}\\= x^{ \frac{3}{2} - \frac{2}{3} }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)