Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-2}{3}}}{x^{1}}\\= x^{ \frac{-2}{3} - 1 }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
2. \(\dfrac{y^{\frac{-2}{3}}}{y^{-2}}\\= y^{ \frac{-2}{3} - (-2) }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
3. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-5}{4} - \frac{2}{3} }= x^{\frac{-23}{12}}\\=\frac{1}{\sqrt[12]{ x^{23} }}\\=\frac{1}{|x|.\sqrt[12]{ x^{11} }}=\frac{1}{|x|.\sqrt[12]{ x^{11} }} \color{purple}{\frac{\sqrt[12]{ x }}{\sqrt[12]{ x }}} \\=\frac{\sqrt[12]{ x }}{|x^{2}|}\\---------------\)
4. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{1}{2} - (\frac{-5}{2}) }= y^{3}\\\\---------------\)
5. \(\dfrac{a^{-1}}{a^{-1}}\\= a^{ -1 - (-1) }= a^{0}\\=1\\---------------\)
6. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{-2}{5}}}\\= x^{ \frac{2}{3} - (\frac{-2}{5}) }= x^{\frac{16}{15}}\\=\sqrt[15]{ x^{16} }=x.\sqrt[15]{ x }\\---------------\)
7. \(\dfrac{q^{1}}{q^{\frac{3}{2}}}\\= q^{ 1 - \frac{3}{2} }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
8. \(\dfrac{q^{\frac{3}{5}}}{q^{1}}\\= q^{ \frac{3}{5} - 1 }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
9. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{1}{4}}}\\= y^{ \frac{2}{5} - \frac{1}{4} }= y^{\frac{3}{20}}\\=\sqrt[20]{ y^{3} }\\---------------\)
10. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{-5}{4} - (\frac{-4}{3}) }= x^{\frac{1}{12}}\\=\sqrt[12]{ x }\\---------------\)
11. \(\dfrac{a^{\frac{-1}{6}}}{a^{-2}}\\= a^{ \frac{-1}{6} - (-2) }= a^{\frac{11}{6}}\\=\sqrt[6]{ a^{11} }=|a|.\sqrt[6]{ a^{5} }\\---------------\)
12. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{3}{4}}}\\= x^{ \frac{3}{5} - \frac{3}{4} }= x^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ x^{3} }}=\frac{1}{\sqrt[20]{ x^{3} }}. \color{purple}{\frac{\sqrt[20]{ x^{17} }}{\sqrt[20]{ x^{17} }}} \\=\frac{\sqrt[20]{ x^{17} }}{|x|}\\---------------\)