Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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