Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{2}}{y^{\frac{5}{6}}}\\= y^{ 2 - \frac{5}{6} }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)
2. \(\dfrac{q^{1}}{q^{\frac{-2}{3}}}\\= q^{ 1 - (\frac{-2}{3}) }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
3. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-5}{3}}}\\= a^{ \frac{2}{3} - (\frac{-5}{3}) }= a^{\frac{7}{3}}\\=\sqrt[3]{ a^{7} }=a^{2}.\sqrt[3]{ a }\\---------------\)
4. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{2}{3}}}\\= a^{ \frac{4}{5} - \frac{2}{3} }= a^{\frac{2}{15}}\\=\sqrt[15]{ a^{2} }\\---------------\)
5. \(\dfrac{q^{1}}{q^{-1}}\\= q^{ 1 - (-1) }= q^{2}\\\\---------------\)
6. \(\dfrac{a^{1}}{a^{\frac{5}{2}}}\\= a^{ 1 - \frac{5}{2} }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
7. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{2}{3} - (\frac{-5}{4}) }= a^{\frac{23}{12}}\\=\sqrt[12]{ a^{23} }=|a|.\sqrt[12]{ a^{11} }\\---------------\)
8. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{2}{3}}}\\= a^{ \frac{1}{4} - \frac{2}{3} }= a^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ a^{5} }}=\frac{1}{\sqrt[12]{ a^{5} }}. \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a|}\\---------------\)
9. \(\dfrac{x^{\frac{-1}{2}}}{x^{-1}}\\= x^{ \frac{-1}{2} - (-1) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
10. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{5}{2}}}\\= q^{ \frac{1}{2} - \frac{5}{2} }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
11. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{1}{3}}}\\= x^{ \frac{2}{3} - \frac{1}{3} }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
12. \(\dfrac{a^{1}}{a^{\frac{-1}{2}}}\\= a^{ 1 - (\frac{-1}{2}) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)