Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{2}{5}}}\\= a^{ \frac{-1}{4} - \frac{2}{5} }= a^{\frac{-13}{20}}\\=\frac{1}{\sqrt[20]{ a^{13} }}=\frac{1}{\sqrt[20]{ a^{13} }}. \color{purple}{\frac{\sqrt[20]{ a^{7} }}{\sqrt[20]{ a^{7} }}} \\=\frac{\sqrt[20]{ a^{7} }}{|a|}\\---------------\)
2. \(\dfrac{x^{-2}}{x^{\frac{5}{3}}}\\= x^{ -2 - \frac{5}{3} }= x^{\frac{-11}{3}}\\=\frac{1}{\sqrt[3]{ x^{11} }}\\=\frac{1}{x^{3}.\sqrt[3]{ x^{2} }}=\frac{1}{x^{3}.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{4}}\\---------------\)
3. \(\dfrac{q^{\frac{3}{2}}}{q^{\frac{2}{3}}}\\= q^{ \frac{3}{2} - \frac{2}{3} }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
4. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{2}{3}}}\\= x^{ \frac{1}{2} - \frac{2}{3} }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
5. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-1}{5}}}\\= y^{ \frac{1}{2} - (\frac{-1}{5}) }= y^{\frac{7}{10}}\\=\sqrt[10]{ y^{7} }\\---------------\)
6. \(\dfrac{a^{\frac{3}{2}}}{a^{\frac{-1}{4}}}\\= a^{ \frac{3}{2} - (\frac{-1}{4}) }= a^{\frac{7}{4}}\\=\sqrt[4]{ a^{7} }=|a|.\sqrt[4]{ a^{3} }\\---------------\)
7. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{5}{3} - (\frac{-3}{4}) }= x^{\frac{29}{12}}\\=\sqrt[12]{ x^{29} }=|x^{2}|.\sqrt[12]{ x^{5} }\\---------------\)
8. \(\dfrac{q^{\frac{-4}{3}}}{q^{\frac{5}{3}}}\\= q^{ \frac{-4}{3} - \frac{5}{3} }= q^{-3}\\=\frac{1}{q^{3}}\\---------------\)
9. \(\dfrac{q^{\frac{3}{2}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{3}{2} - (\frac{-2}{3}) }= q^{\frac{13}{6}}\\=\sqrt[6]{ q^{13} }=|q^{2}|.\sqrt[6]{ q }\\---------------\)
10. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-2}{3} - \frac{1}{2} }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
11. \(\dfrac{y^{1}}{y^{\frac{-2}{3}}}\\= y^{ 1 - (\frac{-2}{3}) }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
12. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{5}{4}}}\\= x^{ \frac{3}{2} - \frac{5}{4} }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)