Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{1}}{y^{1}}\\= y^{ 1 - 1 }= y^{0}\\=1\\---------------\)
2. \(\dfrac{x^{\frac{-5}{3}}}{x^{-1}}\\= x^{ \frac{-5}{3} - (-1) }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
3. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{1}{6} - (\frac{-1}{6}) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
4. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{2}{3}}}\\= q^{ \frac{-1}{3} - \frac{2}{3} }= q^{-1}\\=\frac{1}{q}\\---------------\)
5. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{-1}{5}}}\\= y^{ \frac{1}{3} - (\frac{-1}{5}) }= y^{\frac{8}{15}}\\=\sqrt[15]{ y^{8} }\\---------------\)
6. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{-1}{4} - (\frac{-4}{3}) }= x^{\frac{13}{12}}\\=\sqrt[12]{ x^{13} }=|x|.\sqrt[12]{ x }\\---------------\)
7. \(\dfrac{a^{\frac{5}{2}}}{a^{\frac{1}{5}}}\\= a^{ \frac{5}{2} - \frac{1}{5} }= a^{\frac{23}{10}}\\=\sqrt[10]{ a^{23} }=|a^{2}|.\sqrt[10]{ a^{3} }\\---------------\)
8. \(\dfrac{q^{\frac{1}{4}}}{q^{1}}\\= q^{ \frac{1}{4} - 1 }= q^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ q^{3} }}=\frac{1}{\sqrt[4]{ q^{3} }}. \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q|}\\---------------\)
9. \(\dfrac{y^{\frac{-2}{5}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-2}{5} - (\frac{-1}{2}) }= y^{\frac{1}{10}}\\=\sqrt[10]{ y }\\---------------\)
10. \(\dfrac{q^{\frac{-1}{6}}}{q^{-1}}\\= q^{ \frac{-1}{6} - (-1) }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
11. \(\dfrac{y^{\frac{-5}{3}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-5}{3} - \frac{2}{3} }= y^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ y^{7} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y }}=\frac{1}{y^{2}.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{3}}\\---------------\)
12. \(\dfrac{q^{\frac{-5}{4}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-5}{4} - \frac{1}{2} }= q^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[4]{ q^{3} }}=\frac{1}{|q|.\sqrt[4]{ q^{3} }} \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q^{2}|}\\---------------\)