Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{1}{3}}}{a^{1}}\\= a^{ \frac{1}{3} - 1 }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
2. \(\dfrac{q^{\frac{-5}{3}}}{q^{\frac{1}{4}}}\\= q^{ \frac{-5}{3} - \frac{1}{4} }= q^{\frac{-23}{12}}\\=\frac{1}{\sqrt[12]{ q^{23} }}\\=\frac{1}{|q|.\sqrt[12]{ q^{11} }}=\frac{1}{|q|.\sqrt[12]{ q^{11} }} \color{purple}{\frac{\sqrt[12]{ q }}{\sqrt[12]{ q }}} \\=\frac{\sqrt[12]{ q }}{|q^{2}|}\\---------------\)
3. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{1}{5}}}\\= q^{ \frac{-1}{3} - \frac{1}{5} }= q^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ q^{8} }}=\frac{1}{\sqrt[15]{ q^{8} }}. \color{purple}{\frac{\sqrt[15]{ q^{7} }}{\sqrt[15]{ q^{7} }}} \\=\frac{\sqrt[15]{ q^{7} }}{q}\\---------------\)
4. \(\dfrac{y^{1}}{y^{\frac{3}{4}}}\\= y^{ 1 - \frac{3}{4} }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
5. \(\dfrac{a^{\frac{1}{6}}}{a^{1}}\\= a^{ \frac{1}{6} - 1 }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
6. \(\dfrac{x^{\frac{5}{2}}}{x^{\frac{1}{5}}}\\= x^{ \frac{5}{2} - \frac{1}{5} }= x^{\frac{23}{10}}\\=\sqrt[10]{ x^{23} }=|x^{2}|.\sqrt[10]{ x^{3} }\\---------------\)
7. \(\dfrac{x^{1}}{x^{\frac{4}{5}}}\\= x^{ 1 - \frac{4}{5} }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)
8. \(\dfrac{y^{\frac{-5}{2}}}{y^{1}}\\= y^{ \frac{-5}{2} - 1 }= y^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ y^{7} } }\\=\frac{1}{|y^{3}|. \sqrt{ y } }=\frac{1}{|y^{3}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{4}|}\\---------------\)
9. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{-1}{4}}}\\= q^{ \frac{2}{5} - (\frac{-1}{4}) }= q^{\frac{13}{20}}\\=\sqrt[20]{ q^{13} }\\---------------\)
10. \(\dfrac{y^{-1}}{y^{\frac{-2}{5}}}\\= y^{ -1 - (\frac{-2}{5}) }= y^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ y^{3} }}=\frac{1}{\sqrt[5]{ y^{3} }}. \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y}\\---------------\)
11. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-5}{2} - \frac{1}{2} }= q^{-3}\\=\frac{1}{q^{3}}\\---------------\)
12. \(\dfrac{y^{2}}{y^{\frac{1}{2}}}\\= y^{ 2 - \frac{1}{2} }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)