Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-1}{3} - \frac{1}{2} }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
2. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{3}{2}}}\\= a^{ \frac{1}{2} - \frac{3}{2} }= a^{-1}\\=\frac{1}{a}\\---------------\)
3. \(\dfrac{q^{\frac{1}{5}}}{q^{\frac{1}{2}}}\\= q^{ \frac{1}{5} - \frac{1}{2} }= q^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ q^{3} }}=\frac{1}{\sqrt[10]{ q^{3} }}. \color{purple}{\frac{\sqrt[10]{ q^{7} }}{\sqrt[10]{ q^{7} }}} \\=\frac{\sqrt[10]{ q^{7} }}{|q|}\\---------------\)
4. \(\dfrac{y^{-1}}{y^{-1}}\\= y^{ -1 - (-1) }= y^{0}\\=1\\---------------\)
5. \(\dfrac{x^{\frac{-3}{2}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-3}{2} - \frac{1}{3} }= x^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ x^{11} }}\\=\frac{1}{|x|.\sqrt[6]{ x^{5} }}=\frac{1}{|x|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{2}|}\\---------------\)
6. \(\dfrac{x^{\frac{1}{3}}}{x^{1}}\\= x^{ \frac{1}{3} - 1 }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
7. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{3}{5} - (\frac{-1}{2}) }= a^{\frac{11}{10}}\\=\sqrt[10]{ a^{11} }=|a|.\sqrt[10]{ a }\\---------------\)
8. \(\dfrac{x^{\frac{-1}{3}}}{x^{1}}\\= x^{ \frac{-1}{3} - 1 }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
9. \(\dfrac{y^{\frac{-3}{2}}}{y^{\frac{4}{5}}}\\= y^{ \frac{-3}{2} - \frac{4}{5} }= y^{\frac{-23}{10}}\\=\frac{1}{\sqrt[10]{ y^{23} }}\\=\frac{1}{|y^{2}|.\sqrt[10]{ y^{3} }}=\frac{1}{|y^{2}|.\sqrt[10]{ y^{3} }} \color{purple}{\frac{\sqrt[10]{ y^{7} }}{\sqrt[10]{ y^{7} }}} \\=\frac{\sqrt[10]{ y^{7} }}{|y^{3}|}\\---------------\)
10. \(\dfrac{a^{\frac{3}{4}}}{a^{\frac{1}{2}}}\\= a^{ \frac{3}{4} - \frac{1}{2} }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
11. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{-5}{4} - (\frac{-2}{3}) }= x^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ x^{7} }}=\frac{1}{\sqrt[12]{ x^{7} }}. \color{purple}{\frac{\sqrt[12]{ x^{5} }}{\sqrt[12]{ x^{5} }}} \\=\frac{\sqrt[12]{ x^{5} }}{|x|}\\---------------\)
12. \(\dfrac{q^{\frac{-3}{4}}}{q^{-2}}\\= q^{ \frac{-3}{4} - (-2) }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)