Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{1}{5}}}{y^{\frac{-5}{4}}}\\= y^{ \frac{1}{5} - (\frac{-5}{4}) }= y^{\frac{29}{20}}\\=\sqrt[20]{ y^{29} }=|y|.\sqrt[20]{ y^{9} }\\---------------\)
2. \(\dfrac{q^{\frac{5}{2}}}{q^{\frac{3}{2}}}\\= q^{ \frac{5}{2} - \frac{3}{2} }= q^{1}\\\\---------------\)
3. \(\dfrac{q^{1}}{q^{\frac{-2}{5}}}\\= q^{ 1 - (\frac{-2}{5}) }= q^{\frac{7}{5}}\\=\sqrt[5]{ q^{7} }=q.\sqrt[5]{ q^{2} }\\---------------\)
4. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{5}{6}}}\\= y^{ \frac{-2}{3} - \frac{5}{6} }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
5. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{-5}{3}}}\\= x^{ \frac{-5}{4} - (\frac{-5}{3}) }= x^{\frac{5}{12}}\\=\sqrt[12]{ x^{5} }\\---------------\)
6. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{2}{5}}}\\= y^{ \frac{-3}{4} - \frac{2}{5} }= y^{\frac{-23}{20}}\\=\frac{1}{\sqrt[20]{ y^{23} }}\\=\frac{1}{|y|.\sqrt[20]{ y^{3} }}=\frac{1}{|y|.\sqrt[20]{ y^{3} }} \color{purple}{\frac{\sqrt[20]{ y^{17} }}{\sqrt[20]{ y^{17} }}} \\=\frac{\sqrt[20]{ y^{17} }}{|y^{2}|}\\---------------\)
7. \(\dfrac{y^{\frac{5}{3}}}{y^{\frac{3}{4}}}\\= y^{ \frac{5}{3} - \frac{3}{4} }= y^{\frac{11}{12}}\\=\sqrt[12]{ y^{11} }\\---------------\)
8. \(\dfrac{y^{\frac{-1}{2}}}{y^{1}}\\= y^{ \frac{-1}{2} - 1 }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
9. \(\dfrac{x^{\frac{-5}{4}}}{x^{2}}\\= x^{ \frac{-5}{4} - 2 }= x^{\frac{-13}{4}}\\=\frac{1}{\sqrt[4]{ x^{13} }}\\=\frac{1}{|x^{3}|.\sqrt[4]{ x }}=\frac{1}{|x^{3}|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{4}|}\\---------------\)
10. \(\dfrac{a^{-1}}{a^{\frac{-3}{4}}}\\= a^{ -1 - (\frac{-3}{4}) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
11. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{5}{2}}}\\= y^{ \frac{-4}{3} - \frac{5}{2} }= y^{\frac{-23}{6}}\\=\frac{1}{\sqrt[6]{ y^{23} }}\\=\frac{1}{|y^{3}|.\sqrt[6]{ y^{5} }}=\frac{1}{|y^{3}|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{4}|}\\---------------\)
12. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-3}{2}}}\\= q^{ \frac{-1}{3} - (\frac{-3}{2}) }= q^{\frac{7}{6}}\\=\sqrt[6]{ q^{7} }=|q|.\sqrt[6]{ q }\\---------------\)