Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{-2}{3} - (\frac{-4}{5}) }= q^{\frac{2}{15}}\\=\sqrt[15]{ q^{2} }\\---------------\)
2. \(\dfrac{y^{\frac{1}{6}}}{y^{\frac{1}{5}}}\\= y^{ \frac{1}{6} - \frac{1}{5} }= y^{\frac{-1}{30}}\\=\frac{1}{\sqrt[30]{ y }}=\frac{1}{\sqrt[30]{ y }}. \color{purple}{\frac{\sqrt[30]{ y^{29} }}{\sqrt[30]{ y^{29} }}} \\=\frac{\sqrt[30]{ y^{29} }}{|y|}\\---------------\)
3. \(\dfrac{x^{\frac{2}{3}}}{x^{-1}}\\= x^{ \frac{2}{3} - (-1) }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)
4. \(\dfrac{y^{\frac{5}{4}}}{y^{\frac{-3}{2}}}\\= y^{ \frac{5}{4} - (\frac{-3}{2}) }= y^{\frac{11}{4}}\\=\sqrt[4]{ y^{11} }=|y^{2}|.\sqrt[4]{ y^{3} }\\---------------\)
5. \(\dfrac{q^{1}}{q^{-1}}\\= q^{ 1 - (-1) }= q^{2}\\\\---------------\)
6. \(\dfrac{x^{1}}{x^{\frac{-3}{4}}}\\= x^{ 1 - (\frac{-3}{4}) }= x^{\frac{7}{4}}\\=\sqrt[4]{ x^{7} }=|x|.\sqrt[4]{ x^{3} }\\---------------\)
7. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{-1}{2} - (\frac{-5}{2}) }= x^{2}\\\\---------------\)
8. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{1}{2}}}\\= x^{ \frac{3}{4} - \frac{1}{2} }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
9. \(\dfrac{q^{\frac{-5}{4}}}{q^{\frac{-3}{2}}}\\= q^{ \frac{-5}{4} - (\frac{-3}{2}) }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
10. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{3}{5}}}\\= y^{ \frac{-1}{2} - \frac{3}{5} }= y^{\frac{-11}{10}}\\=\frac{1}{\sqrt[10]{ y^{11} }}\\=\frac{1}{|y|.\sqrt[10]{ y }}=\frac{1}{|y|.\sqrt[10]{ y }} \color{purple}{\frac{\sqrt[10]{ y^{9} }}{\sqrt[10]{ y^{9} }}} \\=\frac{\sqrt[10]{ y^{9} }}{|y^{2}|}\\---------------\)
11. \(\dfrac{a^{\frac{-5}{4}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-5}{4} - (\frac{-1}{2}) }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
12. \(\dfrac{y^{\frac{-5}{3}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-5}{3} - \frac{1}{2} }= y^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ y^{13} }}\\=\frac{1}{|y^{2}|.\sqrt[6]{ y }}=\frac{1}{|y^{2}|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{3}|}\\---------------\)