Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{1}{2} - (\frac{-4}{5}) }= a^{\frac{13}{10}}\\=\sqrt[10]{ a^{13} }=|a|.\sqrt[10]{ a^{3} }\\---------------\)
2. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{2}{5}}}\\= q^{ \frac{-3}{5} - \frac{2}{5} }= q^{-1}\\=\frac{1}{q}\\---------------\)
3. \(\dfrac{a^{\frac{-1}{6}}}{a^{\frac{5}{6}}}\\= a^{ \frac{-1}{6} - \frac{5}{6} }= a^{-1}\\=\frac{1}{a}\\---------------\)
4. \(\dfrac{y^{\frac{-4}{5}}}{y^{1}}\\= y^{ \frac{-4}{5} - 1 }= y^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ y^{9} }}\\=\frac{1}{y.\sqrt[5]{ y^{4} }}=\frac{1}{y.\sqrt[5]{ y^{4} }} \color{purple}{\frac{\sqrt[5]{ y }}{\sqrt[5]{ y }}} \\=\frac{\sqrt[5]{ y }}{y^{2}}\\---------------\)
5. \(\dfrac{a^{\frac{-4}{3}}}{a^{\frac{2}{5}}}\\= a^{ \frac{-4}{3} - \frac{2}{5} }= a^{\frac{-26}{15}}\\=\frac{1}{\sqrt[15]{ a^{26} }}\\=\frac{1}{a.\sqrt[15]{ a^{11} }}=\frac{1}{a.\sqrt[15]{ a^{11} }} \color{purple}{\frac{\sqrt[15]{ a^{4} }}{\sqrt[15]{ a^{4} }}} \\=\frac{\sqrt[15]{ a^{4} }}{a^{2}}\\---------------\)
6. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{1}{6}}}\\= q^{ \frac{-3}{5} - \frac{1}{6} }= q^{\frac{-23}{30}}\\=\frac{1}{\sqrt[30]{ q^{23} }}=\frac{1}{\sqrt[30]{ q^{23} }}. \color{purple}{\frac{\sqrt[30]{ q^{7} }}{\sqrt[30]{ q^{7} }}} \\=\frac{\sqrt[30]{ q^{7} }}{|q|}\\---------------\)
7. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-1}{4}}}\\= y^{ \frac{-1}{3} - (\frac{-1}{4}) }= y^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ y }}=\frac{1}{\sqrt[12]{ y }}. \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y|}\\---------------\)
8. \(\dfrac{x^{\frac{5}{6}}}{x^{\frac{1}{2}}}\\= x^{ \frac{5}{6} - \frac{1}{2} }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
9. \(\dfrac{x^{\frac{-3}{4}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{-3}{4} - (\frac{-5}{2}) }= x^{\frac{7}{4}}\\=\sqrt[4]{ x^{7} }=|x|.\sqrt[4]{ x^{3} }\\---------------\)
10. \(\dfrac{q^{\frac{5}{4}}}{q^{\frac{4}{3}}}\\= q^{ \frac{5}{4} - \frac{4}{3} }= q^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ q }}=\frac{1}{\sqrt[12]{ q }}. \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q|}\\---------------\)
11. \(\dfrac{x^{-1}}{x^{1}}\\= x^{ -1 - 1 }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
12. \(\dfrac{a^{\frac{-5}{2}}}{a^{\frac{3}{5}}}\\= a^{ \frac{-5}{2} - \frac{3}{5} }= a^{\frac{-31}{10}}\\=\frac{1}{\sqrt[10]{ a^{31} }}\\=\frac{1}{|a^{3}|.\sqrt[10]{ a }}=\frac{1}{|a^{3}|.\sqrt[10]{ a }} \color{purple}{\frac{\sqrt[10]{ a^{9} }}{\sqrt[10]{ a^{9} }}} \\=\frac{\sqrt[10]{ a^{9} }}{|a^{4}|}\\---------------\)