Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{-1}}{x^{1}}\\= x^{ -1 - 1 }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
2. \(\dfrac{y^{\frac{-2}{3}}}{y^{1}}\\= y^{ \frac{-2}{3} - 1 }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
3. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{4}{3}}}\\= x^{ \frac{-4}{3} - \frac{4}{3} }= x^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ x^{8} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x^{2} }}=\frac{1}{x^{2}.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{3}}\\---------------\)
4. \(\dfrac{a^{1}}{a^{-1}}\\= a^{ 1 - (-1) }= a^{2}\\\\---------------\)
5. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-2}{3} - \frac{2}{3} }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
6. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{5}{4}}}\\= x^{ \frac{-1}{3} - \frac{5}{4} }= x^{\frac{-19}{12}}\\=\frac{1}{\sqrt[12]{ x^{19} }}\\=\frac{1}{|x|.\sqrt[12]{ x^{7} }}=\frac{1}{|x|.\sqrt[12]{ x^{7} }} \color{purple}{\frac{\sqrt[12]{ x^{5} }}{\sqrt[12]{ x^{5} }}} \\=\frac{\sqrt[12]{ x^{5} }}{|x^{2}|}\\---------------\)
7. \(\dfrac{q^{\frac{4}{3}}}{q^{\frac{1}{2}}}\\= q^{ \frac{4}{3} - \frac{1}{2} }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
8. \(\dfrac{y^{\frac{-4}{3}}}{y^{-1}}\\= y^{ \frac{-4}{3} - (-1) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
9. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-1}{2} - (\frac{-1}{2}) }= a^{0}\\=1\\---------------\)
10. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{1}{3}}}\\= a^{ \frac{1}{3} - \frac{1}{3} }= a^{0}\\=1\\---------------\)
11. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{-2}{5}}}\\= x^{ \frac{-5}{4} - (\frac{-2}{5}) }= x^{\frac{-17}{20}}\\=\frac{1}{\sqrt[20]{ x^{17} }}=\frac{1}{\sqrt[20]{ x^{17} }}. \color{purple}{\frac{\sqrt[20]{ x^{3} }}{\sqrt[20]{ x^{3} }}} \\=\frac{\sqrt[20]{ x^{3} }}{|x|}\\---------------\)
12. \(\dfrac{a^{-1}}{a^{\frac{-2}{3}}}\\= a^{ -1 - (\frac{-2}{3}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)