Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-4}{5}}}{a^{\frac{-5}{3}}}\\= a^{ \frac{-4}{5} - (\frac{-5}{3}) }= a^{\frac{13}{15}}\\=\sqrt[15]{ a^{13} }\\---------------\)
2. \(\dfrac{q^{-2}}{q^{\frac{3}{5}}}\\= q^{ -2 - \frac{3}{5} }= q^{\frac{-13}{5}}\\=\frac{1}{\sqrt[5]{ q^{13} }}\\=\frac{1}{q^{2}.\sqrt[5]{ q^{3} }}=\frac{1}{q^{2}.\sqrt[5]{ q^{3} }} \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q^{3}}\\---------------\)
3. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{-1}{2} - (\frac{-4}{5}) }= q^{\frac{3}{10}}\\=\sqrt[10]{ q^{3} }\\---------------\)
4. \(\dfrac{q^{1}}{q^{\frac{1}{3}}}\\= q^{ 1 - \frac{1}{3} }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
5. \(\dfrac{a^{\frac{-1}{3}}}{a^{-2}}\\= a^{ \frac{-1}{3} - (-2) }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
6. \(\dfrac{a^{\frac{-5}{2}}}{a^{\frac{2}{5}}}\\= a^{ \frac{-5}{2} - \frac{2}{5} }= a^{\frac{-29}{10}}\\=\frac{1}{\sqrt[10]{ a^{29} }}\\=\frac{1}{|a^{2}|.\sqrt[10]{ a^{9} }}=\frac{1}{|a^{2}|.\sqrt[10]{ a^{9} }} \color{purple}{\frac{\sqrt[10]{ a }}{\sqrt[10]{ a }}} \\=\frac{\sqrt[10]{ a }}{|a^{3}|}\\---------------\)
7. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{1}{2}}}\\= q^{ \frac{2}{3} - \frac{1}{2} }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
8. \(\dfrac{q^{\frac{4}{5}}}{q^{\frac{1}{3}}}\\= q^{ \frac{4}{5} - \frac{1}{3} }= q^{\frac{7}{15}}\\=\sqrt[15]{ q^{7} }\\---------------\)
9. \(\dfrac{x^{\frac{2}{5}}}{x^{\frac{-1}{6}}}\\= x^{ \frac{2}{5} - (\frac{-1}{6}) }= x^{\frac{17}{30}}\\=\sqrt[30]{ x^{17} }\\---------------\)
10. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-4}{3} - (\frac{-1}{2}) }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
11. \(\dfrac{a^{\frac{-4}{5}}}{a^{1}}\\= a^{ \frac{-4}{5} - 1 }= a^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ a^{9} }}\\=\frac{1}{a.\sqrt[5]{ a^{4} }}=\frac{1}{a.\sqrt[5]{ a^{4} }} \color{purple}{\frac{\sqrt[5]{ a }}{\sqrt[5]{ a }}} \\=\frac{\sqrt[5]{ a }}{a^{2}}\\---------------\)
12. \(\dfrac{q^{\frac{-5}{3}}}{q^{\frac{3}{4}}}\\= q^{ \frac{-5}{3} - \frac{3}{4} }= q^{\frac{-29}{12}}\\=\frac{1}{\sqrt[12]{ q^{29} }}\\=\frac{1}{|q^{2}|.\sqrt[12]{ q^{5} }}=\frac{1}{|q^{2}|.\sqrt[12]{ q^{5} }} \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q^{3}|}\\---------------\)