Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{-1}{4} - (\frac{-3}{4}) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
2. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{4}{5}}}\\= q^{ \frac{-3}{4} - \frac{4}{5} }= q^{\frac{-31}{20}}\\=\frac{1}{\sqrt[20]{ q^{31} }}\\=\frac{1}{|q|.\sqrt[20]{ q^{11} }}=\frac{1}{|q|.\sqrt[20]{ q^{11} }} \color{purple}{\frac{\sqrt[20]{ q^{9} }}{\sqrt[20]{ q^{9} }}} \\=\frac{\sqrt[20]{ q^{9} }}{|q^{2}|}\\---------------\)
3. \(\dfrac{y^{\frac{-1}{3}}}{y^{-1}}\\= y^{ \frac{-1}{3} - (-1) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
4. \(\dfrac{x^{\frac{5}{6}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{5}{6} - (\frac{-1}{3}) }= x^{\frac{7}{6}}\\=\sqrt[6]{ x^{7} }=|x|.\sqrt[6]{ x }\\---------------\)
5. \(\dfrac{q^{\frac{3}{5}}}{q^{\frac{5}{3}}}\\= q^{ \frac{3}{5} - \frac{5}{3} }= q^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ q^{16} }}\\=\frac{1}{q.\sqrt[15]{ q }}=\frac{1}{q.\sqrt[15]{ q }} \color{purple}{\frac{\sqrt[15]{ q^{14} }}{\sqrt[15]{ q^{14} }}} \\=\frac{\sqrt[15]{ q^{14} }}{q^{2}}\\---------------\)
6. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{2}{3}}}\\= x^{ \frac{3}{4} - \frac{2}{3} }= x^{\frac{1}{12}}\\=\sqrt[12]{ x }\\---------------\)
7. \(\dfrac{q^{-1}}{q^{1}}\\= q^{ -1 - 1 }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
8. \(\dfrac{x^{\frac{-3}{2}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{-3}{2} - (\frac{-5}{4}) }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
9. \(\dfrac{q^{1}}{q^{\frac{-2}{3}}}\\= q^{ 1 - (\frac{-2}{3}) }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
10. \(\dfrac{x^{1}}{x^{\frac{5}{2}}}\\= x^{ 1 - \frac{5}{2} }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
11. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{1}{3}}}\\= q^{ \frac{-3}{4} - \frac{1}{3} }= q^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ q^{13} }}\\=\frac{1}{|q|.\sqrt[12]{ q }}=\frac{1}{|q|.\sqrt[12]{ q }} \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q^{2}|}\\---------------\)
12. \(\dfrac{y^{1}}{y^{\frac{-4}{5}}}\\= y^{ 1 - (\frac{-4}{5}) }= y^{\frac{9}{5}}\\=\sqrt[5]{ y^{9} }=y.\sqrt[5]{ y^{4} }\\---------------\)