Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{1}}{q^{\frac{3}{5}}}\\= q^{ 1 - \frac{3}{5} }= q^{\frac{2}{5}}\\=\sqrt[5]{ q^{2} }\\---------------\)
2. \(\dfrac{q^{\frac{5}{2}}}{q^{\frac{3}{5}}}\\= q^{ \frac{5}{2} - \frac{3}{5} }= q^{\frac{19}{10}}\\=\sqrt[10]{ q^{19} }=|q|.\sqrt[10]{ q^{9} }\\---------------\)
3. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{1}{5}}}\\= a^{ \frac{1}{2} - \frac{1}{5} }= a^{\frac{3}{10}}\\=\sqrt[10]{ a^{3} }\\---------------\)
4. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{2}{5} - (\frac{-1}{3}) }= q^{\frac{11}{15}}\\=\sqrt[15]{ q^{11} }\\---------------\)
5. \(\dfrac{y^{2}}{y^{\frac{-2}{3}}}\\= y^{ 2 - (\frac{-2}{3}) }= y^{\frac{8}{3}}\\=\sqrt[3]{ y^{8} }=y^{2}.\sqrt[3]{ y^{2} }\\---------------\)
6. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-2}{3} - \frac{2}{3} }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
7. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{1}{6}}}\\= x^{ \frac{-2}{3} - \frac{1}{6} }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
8. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{5}{2}}}\\= y^{ \frac{-1}{2} - \frac{5}{2} }= y^{-3}\\=\frac{1}{y^{3}}\\---------------\)
9. \(\dfrac{q^{\frac{1}{5}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{1}{5} - (\frac{-1}{6}) }= q^{\frac{11}{30}}\\=\sqrt[30]{ q^{11} }\\---------------\)
10. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{-1}{2} - (\frac{-5}{4}) }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
11. \(\dfrac{a^{\frac{-3}{2}}}{a^{\frac{-3}{2}}}\\= a^{ \frac{-3}{2} - (\frac{-3}{2}) }= a^{0}\\=1\\---------------\)
12. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-3}{4}}}\\= a^{ \frac{2}{3} - (\frac{-3}{4}) }= a^{\frac{17}{12}}\\=\sqrt[12]{ a^{17} }=|a|.\sqrt[12]{ a^{5} }\\---------------\)