Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-1}{5} - \frac{2}{3} }= y^{\frac{-13}{15}}\\=\frac{1}{\sqrt[15]{ y^{13} }}=\frac{1}{\sqrt[15]{ y^{13} }}. \color{purple}{\frac{\sqrt[15]{ y^{2} }}{\sqrt[15]{ y^{2} }}} \\=\frac{\sqrt[15]{ y^{2} }}{y}\\---------------\)
2. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{-4}{5}}}\\= y^{ \frac{1}{4} - (\frac{-4}{5}) }= y^{\frac{21}{20}}\\=\sqrt[20]{ y^{21} }=|y|.\sqrt[20]{ y }\\---------------\)
3. \(\dfrac{y^{\frac{-3}{2}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-3}{2} - (\frac{-1}{2}) }= y^{-1}\\=\frac{1}{y}\\---------------\)
4. \(\dfrac{y^{1}}{y^{\frac{5}{2}}}\\= y^{ 1 - \frac{5}{2} }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
5. \(\dfrac{y^{\frac{-3}{4}}}{y^{-1}}\\= y^{ \frac{-3}{4} - (-1) }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
6. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{1}{5}}}\\= x^{ \frac{1}{2} - \frac{1}{5} }= x^{\frac{3}{10}}\\=\sqrt[10]{ x^{3} }\\---------------\)
7. \(\dfrac{x^{-1}}{x^{\frac{1}{5}}}\\= x^{ -1 - \frac{1}{5} }= x^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ x^{6} }}\\=\frac{1}{x.\sqrt[5]{ x }}=\frac{1}{x.\sqrt[5]{ x }} \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x^{2}}\\---------------\)
8. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{1}{2} - (\frac{-1}{2}) }= a^{1}\\\\---------------\)
9. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{2}{3} - (\frac{-2}{5}) }= q^{\frac{16}{15}}\\=\sqrt[15]{ q^{16} }=q.\sqrt[15]{ q }\\---------------\)
10. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{2}{3}}}\\= q^{ \frac{1}{3} - \frac{2}{3} }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
11. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{1}{2}}}\\= q^{ \frac{1}{2} - \frac{1}{2} }= q^{0}\\=1\\---------------\)
12. \(\dfrac{a^{\frac{-3}{5}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-3}{5} - \frac{1}{2} }= a^{\frac{-11}{10}}\\=\frac{1}{\sqrt[10]{ a^{11} }}\\=\frac{1}{|a|.\sqrt[10]{ a }}=\frac{1}{|a|.\sqrt[10]{ a }} \color{purple}{\frac{\sqrt[10]{ a^{9} }}{\sqrt[10]{ a^{9} }}} \\=\frac{\sqrt[10]{ a^{9} }}{|a^{2}|}\\---------------\)