Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-2}{3} - \frac{1}{2} }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)
2. \(\dfrac{y^{-1}}{y^{\frac{1}{2}}}\\= y^{ -1 - \frac{1}{2} }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
3. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{1}{2}}}\\= q^{ \frac{1}{2} - \frac{1}{2} }= q^{0}\\=1\\---------------\)
4. \(\dfrac{a^{2}}{a^{\frac{5}{6}}}\\= a^{ 2 - \frac{5}{6} }= a^{\frac{7}{6}}\\=\sqrt[6]{ a^{7} }=|a|.\sqrt[6]{ a }\\---------------\)
5. \(\dfrac{a^{\frac{-5}{4}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-5}{4} - \frac{2}{3} }= a^{\frac{-23}{12}}\\=\frac{1}{\sqrt[12]{ a^{23} }}\\=\frac{1}{|a|.\sqrt[12]{ a^{11} }}=\frac{1}{|a|.\sqrt[12]{ a^{11} }} \color{purple}{\frac{\sqrt[12]{ a }}{\sqrt[12]{ a }}} \\=\frac{\sqrt[12]{ a }}{|a^{2}|}\\---------------\)
6. \(\dfrac{a^{\frac{4}{3}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{4}{3} - (\frac{-1}{3}) }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
7. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{3}{2}}}\\= a^{ \frac{-1}{3} - \frac{3}{2} }= a^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ a^{11} }}\\=\frac{1}{|a|.\sqrt[6]{ a^{5} }}=\frac{1}{|a|.\sqrt[6]{ a^{5} }} \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a^{2}|}\\---------------\)
8. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{5}{2}}}\\= q^{ \frac{1}{3} - \frac{5}{2} }= q^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ q^{13} }}\\=\frac{1}{|q^{2}|.\sqrt[6]{ q }}=\frac{1}{|q^{2}|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{3}|}\\---------------\)
9. \(\dfrac{a^{\frac{-5}{4}}}{a^{1}}\\= a^{ \frac{-5}{4} - 1 }= a^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ a^{9} }}\\=\frac{1}{|a^{2}|.\sqrt[4]{ a }}=\frac{1}{|a^{2}|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{3}|}\\---------------\)
10. \(\dfrac{q^{\frac{-5}{6}}}{q^{\frac{4}{3}}}\\= q^{ \frac{-5}{6} - \frac{4}{3} }= q^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ q^{13} }}\\=\frac{1}{|q^{2}|.\sqrt[6]{ q }}=\frac{1}{|q^{2}|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{3}|}\\---------------\)
11. \(\dfrac{y^{\frac{5}{6}}}{y^{\frac{5}{4}}}\\= y^{ \frac{5}{6} - \frac{5}{4} }= y^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ y^{5} }}=\frac{1}{\sqrt[12]{ y^{5} }}. \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y|}\\---------------\)
12. \(\dfrac{a^{\frac{3}{2}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{3}{2} - (\frac{-5}{4}) }= a^{\frac{11}{4}}\\=\sqrt[4]{ a^{11} }=|a^{2}|.\sqrt[4]{ a^{3} }\\---------------\)