Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{-1}{5}}}\\= a^{ \frac{4}{5} - (\frac{-1}{5}) }= a^{1}\\\\---------------\)
2. \(\dfrac{q^{\frac{4}{5}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{4}{5} - (\frac{-1}{2}) }= q^{\frac{13}{10}}\\=\sqrt[10]{ q^{13} }=|q|.\sqrt[10]{ q^{3} }\\---------------\)
3. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{2}{5}}}\\= a^{ \frac{-1}{2} - \frac{2}{5} }= a^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ a^{9} }}=\frac{1}{\sqrt[10]{ a^{9} }}. \color{purple}{\frac{\sqrt[10]{ a }}{\sqrt[10]{ a }}} \\=\frac{\sqrt[10]{ a }}{|a|}\\---------------\)
4. \(\dfrac{x^{\frac{-3}{4}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-3}{4} - \frac{1}{3} }= x^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ x^{13} }}\\=\frac{1}{|x|.\sqrt[12]{ x }}=\frac{1}{|x|.\sqrt[12]{ x }} \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x^{2}|}\\---------------\)
5. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{3}{2}}}\\= a^{ \frac{2}{3} - \frac{3}{2} }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
6. \(\dfrac{y^{-1}}{y^{\frac{3}{4}}}\\= y^{ -1 - \frac{3}{4} }= y^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[4]{ y^{3} }}=\frac{1}{|y|.\sqrt[4]{ y^{3} }} \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y^{2}|}\\---------------\)
7. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{-1}{3} - (\frac{-1}{5}) }= q^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ q^{2} }}=\frac{1}{\sqrt[15]{ q^{2} }}. \color{purple}{\frac{\sqrt[15]{ q^{13} }}{\sqrt[15]{ q^{13} }}} \\=\frac{\sqrt[15]{ q^{13} }}{q}\\---------------\)
8. \(\dfrac{a^{1}}{a^{\frac{1}{4}}}\\= a^{ 1 - \frac{1}{4} }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
9. \(\dfrac{y^{1}}{y^{-1}}\\= y^{ 1 - (-1) }= y^{2}\\\\---------------\)
10. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{2}{3} - (\frac{-3}{5}) }= x^{\frac{19}{15}}\\=\sqrt[15]{ x^{19} }=x.\sqrt[15]{ x^{4} }\\---------------\)
11. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{1}{6}}}\\= a^{ \frac{-3}{4} - \frac{1}{6} }= a^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ a^{11} }}=\frac{1}{\sqrt[12]{ a^{11} }}. \color{purple}{\frac{\sqrt[12]{ a }}{\sqrt[12]{ a }}} \\=\frac{\sqrt[12]{ a }}{|a|}\\---------------\)
12. \(\dfrac{q^{-1}}{q^{\frac{-3}{2}}}\\= q^{ -1 - (\frac{-3}{2}) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)