Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{-2}}{q^{-2}}\\= q^{ -2 - (-2) }= q^{0}\\=1\\---------------\)
2. \(\dfrac{a^{1}}{a^{\frac{2}{3}}}\\= a^{ 1 - \frac{2}{3} }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
3. \(\dfrac{q^{\frac{-5}{4}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{-5}{4} - (\frac{-5}{2}) }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
4. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-4}{5} - \frac{1}{2} }= x^{\frac{-13}{10}}\\=\frac{1}{\sqrt[10]{ x^{13} }}\\=\frac{1}{|x|.\sqrt[10]{ x^{3} }}=\frac{1}{|x|.\sqrt[10]{ x^{3} }} \color{purple}{\frac{\sqrt[10]{ x^{7} }}{\sqrt[10]{ x^{7} }}} \\=\frac{\sqrt[10]{ x^{7} }}{|x^{2}|}\\---------------\)
5. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{5}{3}}}\\= a^{ \frac{4}{5} - \frac{5}{3} }= a^{\frac{-13}{15}}\\=\frac{1}{\sqrt[15]{ a^{13} }}=\frac{1}{\sqrt[15]{ a^{13} }}. \color{purple}{\frac{\sqrt[15]{ a^{2} }}{\sqrt[15]{ a^{2} }}} \\=\frac{\sqrt[15]{ a^{2} }}{a}\\---------------\)
6. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{-2}{5}}}\\= x^{ \frac{-2}{3} - (\frac{-2}{5}) }= x^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ x^{4} }}=\frac{1}{\sqrt[15]{ x^{4} }}. \color{purple}{\frac{\sqrt[15]{ x^{11} }}{\sqrt[15]{ x^{11} }}} \\=\frac{\sqrt[15]{ x^{11} }}{x}\\---------------\)
7. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{4}{5}}}\\= x^{ \frac{4}{5} - \frac{4}{5} }= x^{0}\\=1\\---------------\)
8. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{-1}{3} - (\frac{-5}{4}) }= a^{\frac{11}{12}}\\=\sqrt[12]{ a^{11} }\\---------------\)
9. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{5}{6}}}\\= y^{ \frac{5}{2} - \frac{5}{6} }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
10. \(\dfrac{q^{\frac{-4}{5}}}{q^{\frac{5}{4}}}\\= q^{ \frac{-4}{5} - \frac{5}{4} }= q^{\frac{-41}{20}}\\=\frac{1}{\sqrt[20]{ q^{41} }}\\=\frac{1}{|q^{2}|.\sqrt[20]{ q }}=\frac{1}{|q^{2}|.\sqrt[20]{ q }} \color{purple}{\frac{\sqrt[20]{ q^{19} }}{\sqrt[20]{ q^{19} }}} \\=\frac{\sqrt[20]{ q^{19} }}{|q^{3}|}\\---------------\)
11. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{2}{3} - (\frac{-5}{2}) }= q^{\frac{19}{6}}\\=\sqrt[6]{ q^{19} }=|q^{3}|.\sqrt[6]{ q }\\---------------\)
12. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{-1}{2} - (\frac{-5}{2}) }= q^{2}\\\\---------------\)