Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{1}}{a^{1}}\\= a^{ 1 - 1 }= a^{0}\\=1\\---------------\)
2. \(\dfrac{x^{\frac{-3}{2}}}{x^{-1}}\\= x^{ \frac{-3}{2} - (-1) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
3. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{2}{5}}}\\= y^{ \frac{2}{3} - \frac{2}{5} }= y^{\frac{4}{15}}\\=\sqrt[15]{ y^{4} }\\---------------\)
4. \(\dfrac{y^{1}}{y^{-1}}\\= y^{ 1 - (-1) }= y^{2}\\\\---------------\)
5. \(\dfrac{y^{-1}}{y^{\frac{4}{5}}}\\= y^{ -1 - \frac{4}{5} }= y^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ y^{9} }}\\=\frac{1}{y.\sqrt[5]{ y^{4} }}=\frac{1}{y.\sqrt[5]{ y^{4} }} \color{purple}{\frac{\sqrt[5]{ y }}{\sqrt[5]{ y }}} \\=\frac{\sqrt[5]{ y }}{y^{2}}\\---------------\)
6. \(\dfrac{y^{\frac{-1}{6}}}{y^{\frac{-1}{4}}}\\= y^{ \frac{-1}{6} - (\frac{-1}{4}) }= y^{\frac{1}{12}}\\=\sqrt[12]{ y }\\---------------\)
7. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-1}{4} - \frac{2}{3} }= x^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ x^{11} }}=\frac{1}{\sqrt[12]{ x^{11} }}. \color{purple}{\frac{\sqrt[12]{ x }}{\sqrt[12]{ x }}} \\=\frac{\sqrt[12]{ x }}{|x|}\\---------------\)
8. \(\dfrac{x^{\frac{-3}{4}}}{x^{\frac{5}{3}}}\\= x^{ \frac{-3}{4} - \frac{5}{3} }= x^{\frac{-29}{12}}\\=\frac{1}{\sqrt[12]{ x^{29} }}\\=\frac{1}{|x^{2}|.\sqrt[12]{ x^{5} }}=\frac{1}{|x^{2}|.\sqrt[12]{ x^{5} }} \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x^{3}|}\\---------------\)
9. \(\dfrac{x^{\frac{4}{5}}}{x^{-1}}\\= x^{ \frac{4}{5} - (-1) }= x^{\frac{9}{5}}\\=\sqrt[5]{ x^{9} }=x.\sqrt[5]{ x^{4} }\\---------------\)
10. \(\dfrac{q^{\frac{-1}{2}}}{q^{1}}\\= q^{ \frac{-1}{2} - 1 }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
11. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{2}{3}}}\\= a^{ \frac{1}{2} - \frac{2}{3} }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
12. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{1}{5}}}\\= x^{ \frac{5}{3} - \frac{1}{5} }= x^{\frac{22}{15}}\\=\sqrt[15]{ x^{22} }=x.\sqrt[15]{ x^{7} }\\---------------\)