Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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