Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{1}}{y^{-2}}\\= y^{ 1 - (-2) }= y^{3}\\\\---------------\)
2. \(\dfrac{q^{\frac{-4}{5}}}{q^{\frac{5}{3}}}\\= q^{ \frac{-4}{5} - \frac{5}{3} }= q^{\frac{-37}{15}}\\=\frac{1}{\sqrt[15]{ q^{37} }}\\=\frac{1}{q^{2}.\sqrt[15]{ q^{7} }}=\frac{1}{q^{2}.\sqrt[15]{ q^{7} }} \color{purple}{\frac{\sqrt[15]{ q^{8} }}{\sqrt[15]{ q^{8} }}} \\=\frac{\sqrt[15]{ q^{8} }}{q^{3}}\\---------------\)
3. \(\dfrac{y^{\frac{1}{6}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{1}{6} - (\frac{-1}{2}) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
4. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{2}{5}}}\\= x^{ \frac{-1}{2} - \frac{2}{5} }= x^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ x^{9} }}=\frac{1}{\sqrt[10]{ x^{9} }}. \color{purple}{\frac{\sqrt[10]{ x }}{\sqrt[10]{ x }}} \\=\frac{\sqrt[10]{ x }}{|x|}\\---------------\)
5. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-5}{3}}}\\= a^{ \frac{-2}{3} - (\frac{-5}{3}) }= a^{1}\\\\---------------\)
6. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{-1}{3} - (\frac{-1}{3}) }= x^{0}\\=1\\---------------\)
7. \(\dfrac{a^{\frac{5}{6}}}{a^{1}}\\= a^{ \frac{5}{6} - 1 }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
8. \(\dfrac{q^{2}}{q^{\frac{5}{4}}}\\= q^{ 2 - \frac{5}{4} }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
9. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{-1}{4} - (\frac{-2}{5}) }= a^{\frac{3}{20}}\\=\sqrt[20]{ a^{3} }\\---------------\)
10. \(\dfrac{y^{\frac{5}{4}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{5}{4} - (\frac{-2}{3}) }= y^{\frac{23}{12}}\\=\sqrt[12]{ y^{23} }=|y|.\sqrt[12]{ y^{11} }\\---------------\)
11. \(\dfrac{y^{\frac{2}{5}}}{y^{-1}}\\= y^{ \frac{2}{5} - (-1) }= y^{\frac{7}{5}}\\=\sqrt[5]{ y^{7} }=y.\sqrt[5]{ y^{2} }\\---------------\)
12. \(\dfrac{a^{\frac{2}{3}}}{a^{1}}\\= a^{ \frac{2}{3} - 1 }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)