Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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