Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{3}{5}}}\\= q^{ \frac{2}{3} - \frac{3}{5} }= q^{\frac{1}{15}}\\=\sqrt[15]{ q }\\---------------\)
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. \(\dfrac{a^{-1}}{a^{-1}}\\= a^{ -1 - (-1) }= a^{0}\\=1\\---------------\)
4. \(\dfrac{y^{1}}{y^{\frac{-2}{3}}}\\= y^{ 1 - (\frac{-2}{3}) }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
5. \(\dfrac{y^{\frac{-5}{4}}}{y^{1}}\\= y^{ \frac{-5}{4} - 1 }= y^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ y^{9} }}\\=\frac{1}{|y^{2}|.\sqrt[4]{ y }}=\frac{1}{|y^{2}|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{3}|}\\---------------\)
6. \(\dfrac{x^{\frac{-3}{4}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-3}{4} - (\frac{-1}{2}) }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
7. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{-2}{3} - (\frac{-2}{3}) }= x^{0}\\=1\\---------------\)
8. \(\dfrac{q^{\frac{4}{5}}}{q^{\frac{5}{4}}}\\= q^{ \frac{4}{5} - \frac{5}{4} }= q^{\frac{-9}{20}}\\=\frac{1}{\sqrt[20]{ q^{9} }}=\frac{1}{\sqrt[20]{ q^{9} }}. \color{purple}{\frac{\sqrt[20]{ q^{11} }}{\sqrt[20]{ q^{11} }}} \\=\frac{\sqrt[20]{ q^{11} }}{|q|}\\---------------\)
9. \(\dfrac{y^{\frac{-1}{6}}}{y^{1}}\\= y^{ \frac{-1}{6} - 1 }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
10. \(\dfrac{q^{\frac{5}{2}}}{q^{\frac{-3}{5}}}\\= q^{ \frac{5}{2} - (\frac{-3}{5}) }= q^{\frac{31}{10}}\\=\sqrt[10]{ q^{31} }=|q^{3}|.\sqrt[10]{ q }\\---------------\)
11. \(\dfrac{a^{\frac{5}{6}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{5}{6} - (\frac{-5}{4}) }= a^{\frac{25}{12}}\\=\sqrt[12]{ a^{25} }=|a^{2}|.\sqrt[12]{ a }\\---------------\)
12. \(\dfrac{q^{\frac{3}{5}}}{q^{\frac{1}{2}}}\\= q^{ \frac{3}{5} - \frac{1}{2} }= q^{\frac{1}{10}}\\=\sqrt[10]{ q }\\---------------\)