Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{-3}{4}}}\\= y^{ \frac{-4}{5} - (\frac{-3}{4}) }= y^{\frac{-1}{20}}\\=\frac{1}{\sqrt[20]{ y }}=\frac{1}{\sqrt[20]{ y }}. \color{purple}{\frac{\sqrt[20]{ y^{19} }}{\sqrt[20]{ y^{19} }}} \\=\frac{\sqrt[20]{ y^{19} }}{|y|}\\---------------\)
2. \(\dfrac{a^{-2}}{a^{\frac{3}{5}}}\\= a^{ -2 - \frac{3}{5} }= a^{\frac{-13}{5}}\\=\frac{1}{\sqrt[5]{ a^{13} }}\\=\frac{1}{a^{2}.\sqrt[5]{ a^{3} }}=\frac{1}{a^{2}.\sqrt[5]{ a^{3} }} \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a^{3}}\\---------------\)
3. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{2}{3} - (\frac{-5}{2}) }= y^{\frac{19}{6}}\\=\sqrt[6]{ y^{19} }=|y^{3}|.\sqrt[6]{ y }\\---------------\)
4. \(\dfrac{y^{\frac{-2}{5}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{-2}{5} - (\frac{-2}{3}) }= y^{\frac{4}{15}}\\=\sqrt[15]{ y^{4} }\\---------------\)
5. \(\dfrac{y^{\frac{2}{3}}}{y^{-1}}\\= y^{ \frac{2}{3} - (-1) }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
6. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{3}{4}}}\\= a^{ \frac{2}{5} - \frac{3}{4} }= a^{\frac{-7}{20}}\\=\frac{1}{\sqrt[20]{ a^{7} }}=\frac{1}{\sqrt[20]{ a^{7} }}. \color{purple}{\frac{\sqrt[20]{ a^{13} }}{\sqrt[20]{ a^{13} }}} \\=\frac{\sqrt[20]{ a^{13} }}{|a|}\\---------------\)
7. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{-1}{3} - (\frac{-4}{3}) }= y^{1}\\\\---------------\)
8. \(\dfrac{y^{1}}{y^{\frac{1}{2}}}\\= y^{ 1 - \frac{1}{2} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
9. \(\dfrac{x^{-2}}{x^{\frac{5}{2}}}\\= x^{ -2 - \frac{5}{2} }= x^{\frac{-9}{2}}\\=\frac{1}{ \sqrt{ x^{9} } }\\=\frac{1}{|x^{4}|. \sqrt{ x } }=\frac{1}{|x^{4}|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{5}|}\\---------------\)
10. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{3}{5}}}\\= q^{ \frac{5}{6} - \frac{3}{5} }= q^{\frac{7}{30}}\\=\sqrt[30]{ q^{7} }\\---------------\)
11. \(\dfrac{y^{\frac{-1}{5}}}{y^{1}}\\= y^{ \frac{-1}{5} - 1 }= y^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ y^{6} }}\\=\frac{1}{y.\sqrt[5]{ y }}=\frac{1}{y.\sqrt[5]{ y }} \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y^{2}}\\---------------\)
12. \(\dfrac{a^{\frac{1}{6}}}{a^{1}}\\= a^{ \frac{1}{6} - 1 }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)