Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{1}}{y^{-1}}\\= y^{ 1 - (-1) }= y^{2}\\\\---------------\)
2. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-1}{4}}}\\= y^{ \frac{1}{2} - (\frac{-1}{4}) }= y^{\frac{3}{4}}\\=\sqrt[4]{ y^{3} }\\---------------\)
3. \(\dfrac{x^{1}}{x^{\frac{2}{3}}}\\= x^{ 1 - \frac{2}{3} }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
4. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{5}{3}}}\\= x^{ \frac{-2}{3} - \frac{5}{3} }= x^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ x^{7} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x }}=\frac{1}{x^{2}.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{3}}\\---------------\)
5. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{5}{4}}}\\= x^{ \frac{-1}{3} - \frac{5}{4} }= x^{\frac{-19}{12}}\\=\frac{1}{\sqrt[12]{ x^{19} }}\\=\frac{1}{|x|.\sqrt[12]{ x^{7} }}=\frac{1}{|x|.\sqrt[12]{ x^{7} }} \color{purple}{\frac{\sqrt[12]{ x^{5} }}{\sqrt[12]{ x^{5} }}} \\=\frac{\sqrt[12]{ x^{5} }}{|x^{2}|}\\---------------\)
6. \(\dfrac{y^{1}}{y^{\frac{1}{2}}}\\= y^{ 1 - \frac{1}{2} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
7. \(\dfrac{a^{\frac{-5}{4}}}{a^{1}}\\= a^{ \frac{-5}{4} - 1 }= a^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ a^{9} }}\\=\frac{1}{|a^{2}|.\sqrt[4]{ a }}=\frac{1}{|a^{2}|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{3}|}\\---------------\)
8. \(\dfrac{q^{\frac{5}{2}}}{q^{-1}}\\= q^{ \frac{5}{2} - (-1) }= q^{\frac{7}{2}}\\= \sqrt{ q^{7} } =|q^{3}|. \sqrt{ q } \\---------------\)
9. \(\dfrac{a^{\frac{1}{6}}}{a^{\frac{2}{5}}}\\= a^{ \frac{1}{6} - \frac{2}{5} }= a^{\frac{-7}{30}}\\=\frac{1}{\sqrt[30]{ a^{7} }}=\frac{1}{\sqrt[30]{ a^{7} }}. \color{purple}{\frac{\sqrt[30]{ a^{23} }}{\sqrt[30]{ a^{23} }}} \\=\frac{\sqrt[30]{ a^{23} }}{|a|}\\---------------\)
10. \(\dfrac{y^{\frac{1}{6}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{1}{6} - (\frac{-2}{5}) }= y^{\frac{17}{30}}\\=\sqrt[30]{ y^{17} }\\---------------\)
11. \(\dfrac{y^{\frac{1}{4}}}{y^{-2}}\\= y^{ \frac{1}{4} - (-2) }= y^{\frac{9}{4}}\\=\sqrt[4]{ y^{9} }=|y^{2}|.\sqrt[4]{ y }\\---------------\)
12. \(\dfrac{y^{\frac{-3}{2}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{-3}{2} - (\frac{-1}{6}) }= y^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ y^{4} }}\\=\frac{1}{y.\sqrt[3]{ y }}=\frac{1}{y.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{2}}\\---------------\)