Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{5}{3}}}{a^{-2}}\\= a^{ \frac{5}{3} - (-2) }= a^{\frac{11}{3}}\\=\sqrt[3]{ a^{11} }=a^{3}.\sqrt[3]{ a^{2} }\\---------------\)
2. \(\dfrac{q^{\frac{4}{5}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{4}{5} - (\frac{-1}{3}) }= q^{\frac{17}{15}}\\=\sqrt[15]{ q^{17} }=q.\sqrt[15]{ q^{2} }\\---------------\)
3. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{-5}{3}}}\\= a^{ \frac{3}{5} - (\frac{-5}{3}) }= a^{\frac{34}{15}}\\=\sqrt[15]{ a^{34} }=a^{2}.\sqrt[15]{ a^{4} }\\---------------\)
4. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{2}{5}}}\\= q^{ \frac{1}{4} - \frac{2}{5} }= q^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ q^{3} }}=\frac{1}{\sqrt[20]{ q^{3} }}. \color{purple}{\frac{\sqrt[20]{ q^{17} }}{\sqrt[20]{ q^{17} }}} \\=\frac{\sqrt[20]{ q^{17} }}{|q|}\\---------------\)
5. \(\dfrac{q^{\frac{-2}{5}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-2}{5} - (\frac{-1}{2}) }= q^{\frac{1}{10}}\\=\sqrt[10]{ q }\\---------------\)
6. \(\dfrac{a^{\frac{-4}{3}}}{a^{\frac{5}{4}}}\\= a^{ \frac{-4}{3} - \frac{5}{4} }= a^{\frac{-31}{12}}\\=\frac{1}{\sqrt[12]{ a^{31} }}\\=\frac{1}{|a^{2}|.\sqrt[12]{ a^{7} }}=\frac{1}{|a^{2}|.\sqrt[12]{ a^{7} }} \color{purple}{\frac{\sqrt[12]{ a^{5} }}{\sqrt[12]{ a^{5} }}} \\=\frac{\sqrt[12]{ a^{5} }}{|a^{3}|}\\---------------\)
7. \(\dfrac{y^{-1}}{y^{\frac{-1}{5}}}\\= y^{ -1 - (\frac{-1}{5}) }= y^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ y^{4} }}=\frac{1}{\sqrt[5]{ y^{4} }}. \color{purple}{\frac{\sqrt[5]{ y }}{\sqrt[5]{ y }}} \\=\frac{\sqrt[5]{ y }}{y}\\---------------\)
8. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{1}{2}}}\\= y^{ \frac{1}{2} - \frac{1}{2} }= y^{0}\\=1\\---------------\)
9. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{1}{2}}}\\= a^{ \frac{4}{5} - \frac{1}{2} }= a^{\frac{3}{10}}\\=\sqrt[10]{ a^{3} }\\---------------\)
10. \(\dfrac{y^{-1}}{y^{\frac{-3}{2}}}\\= y^{ -1 - (\frac{-3}{2}) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
11. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-5}{4}}}\\= q^{ \frac{1}{2} - (\frac{-5}{4}) }= q^{\frac{7}{4}}\\=\sqrt[4]{ q^{7} }=|q|.\sqrt[4]{ q^{3} }\\---------------\)
12. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{5}{2} - (\frac{-1}{2}) }= y^{3}\\\\---------------\)