Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{1}}{q^{\frac{-1}{2}}}\\= q^{ 1 - (\frac{-1}{2}) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
2. \(\dfrac{a^{\frac{-4}{3}}}{a^{\frac{3}{4}}}\\= a^{ \frac{-4}{3} - \frac{3}{4} }= a^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ a^{25} }}\\=\frac{1}{|a^{2}|.\sqrt[12]{ a }}=\frac{1}{|a^{2}|.\sqrt[12]{ a }} \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a^{3}|}\\---------------\)
3. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{3}{5}}}\\= x^{ \frac{-1}{3} - \frac{3}{5} }= x^{\frac{-14}{15}}\\=\frac{1}{\sqrt[15]{ x^{14} }}=\frac{1}{\sqrt[15]{ x^{14} }}. \color{purple}{\frac{\sqrt[15]{ x }}{\sqrt[15]{ x }}} \\=\frac{\sqrt[15]{ x }}{x}\\---------------\)
4. \(\dfrac{x^{\frac{5}{6}}}{x^{\frac{2}{5}}}\\= x^{ \frac{5}{6} - \frac{2}{5} }= x^{\frac{13}{30}}\\=\sqrt[30]{ x^{13} }\\---------------\)
5. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{1}{5}}}\\= x^{ \frac{-1}{2} - \frac{1}{5} }= x^{\frac{-7}{10}}\\=\frac{1}{\sqrt[10]{ x^{7} }}=\frac{1}{\sqrt[10]{ x^{7} }}. \color{purple}{\frac{\sqrt[10]{ x^{3} }}{\sqrt[10]{ x^{3} }}} \\=\frac{\sqrt[10]{ x^{3} }}{|x|}\\---------------\)
6. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{2}{3}}}\\= y^{ \frac{5}{2} - \frac{2}{3} }= y^{\frac{11}{6}}\\=\sqrt[6]{ y^{11} }=|y|.\sqrt[6]{ y^{5} }\\---------------\)
7. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-2}{3} - (\frac{-1}{2}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
8. \(\dfrac{q^{1}}{q^{\frac{-1}{3}}}\\= q^{ 1 - (\frac{-1}{3}) }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
9. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-4}{5}}}\\= y^{ \frac{1}{2} - (\frac{-4}{5}) }= y^{\frac{13}{10}}\\=\sqrt[10]{ y^{13} }=|y|.\sqrt[10]{ y^{3} }\\---------------\)
10. \(\dfrac{y^{-1}}{y^{-1}}\\= y^{ -1 - (-1) }= y^{0}\\=1\\---------------\)
11. \(\dfrac{a^{-1}}{a^{1}}\\= a^{ -1 - 1 }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
12. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-5}{4}}}\\= q^{ \frac{-1}{2} - (\frac{-5}{4}) }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)