Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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