Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{5}{4}}}\\= q^{ \frac{1}{4} - \frac{5}{4} }= q^{-1}\\=\frac{1}{q}\\---------------\)
2. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-1}{2} - \frac{1}{3} }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
3. \(\dfrac{x^{1}}{x^{\frac{-2}{5}}}\\= x^{ 1 - (\frac{-2}{5}) }= x^{\frac{7}{5}}\\=\sqrt[5]{ x^{7} }=x.\sqrt[5]{ x^{2} }\\---------------\)
4. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{-1}{6}}}\\= x^{ \frac{3}{4} - (\frac{-1}{6}) }= x^{\frac{11}{12}}\\=\sqrt[12]{ x^{11} }\\---------------\)
5. \(\dfrac{y^{1}}{y^{1}}\\= y^{ 1 - 1 }= y^{0}\\=1\\---------------\)
6. \(\dfrac{a^{-1}}{a^{\frac{-1}{2}}}\\= a^{ -1 - (\frac{-1}{2}) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
7. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{4}{5}}}\\= q^{ \frac{-2}{3} - \frac{4}{5} }= q^{\frac{-22}{15}}\\=\frac{1}{\sqrt[15]{ q^{22} }}\\=\frac{1}{q.\sqrt[15]{ q^{7} }}=\frac{1}{q.\sqrt[15]{ q^{7} }} \color{purple}{\frac{\sqrt[15]{ q^{8} }}{\sqrt[15]{ q^{8} }}} \\=\frac{\sqrt[15]{ q^{8} }}{q^{2}}\\---------------\)
8. \(\dfrac{x^{-1}}{x^{\frac{-3}{5}}}\\= x^{ -1 - (\frac{-3}{5}) }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
9. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{3}{2} - (\frac{-2}{3}) }= x^{\frac{13}{6}}\\=\sqrt[6]{ x^{13} }=|x^{2}|.\sqrt[6]{ x }\\---------------\)
10. \(\dfrac{a^{1}}{a^{\frac{1}{4}}}\\= a^{ 1 - \frac{1}{4} }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
11. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{1}{2}}}\\= x^{ \frac{1}{2} - \frac{1}{2} }= x^{0}\\=1\\---------------\)
12. \(\dfrac{y^{1}}{y^{\frac{-5}{3}}}\\= y^{ 1 - (\frac{-5}{3}) }= y^{\frac{8}{3}}\\=\sqrt[3]{ y^{8} }=y^{2}.\sqrt[3]{ y^{2} }\\---------------\)