Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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