Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{-3}{4} - (\frac{-4}{3}) }= q^{\frac{7}{12}}\\=\sqrt[12]{ q^{7} }\\---------------\)
2. \(\dfrac{a^{-1}}{a^{\frac{4}{5}}}\\= a^{ -1 - \frac{4}{5} }= a^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ a^{9} }}\\=\frac{1}{a.\sqrt[5]{ a^{4} }}=\frac{1}{a.\sqrt[5]{ a^{4} }} \color{purple}{\frac{\sqrt[5]{ a }}{\sqrt[5]{ a }}} \\=\frac{\sqrt[5]{ a }}{a^{2}}\\---------------\)
3. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{4}{3}}}\\= x^{ \frac{-4}{5} - \frac{4}{3} }= x^{\frac{-32}{15}}\\=\frac{1}{\sqrt[15]{ x^{32} }}\\=\frac{1}{x^{2}.\sqrt[15]{ x^{2} }}=\frac{1}{x^{2}.\sqrt[15]{ x^{2} }} \color{purple}{\frac{\sqrt[15]{ x^{13} }}{\sqrt[15]{ x^{13} }}} \\=\frac{\sqrt[15]{ x^{13} }}{x^{3}}\\---------------\)
4. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-2}{3} - \frac{1}{2} }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)
5. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{5}{6}}}\\= q^{ \frac{1}{2} - \frac{5}{6} }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
6. \(\dfrac{x^{1}}{x^{1}}\\= x^{ 1 - 1 }= x^{0}\\=1\\---------------\)
7. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{2}{3} - (\frac{-5}{4}) }= x^{\frac{23}{12}}\\=\sqrt[12]{ x^{23} }=|x|.\sqrt[12]{ x^{11} }\\---------------\)
8. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{4}{3}}}\\= x^{ \frac{1}{2} - \frac{4}{3} }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
9. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-1}{3} - \frac{1}{3} }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
10. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{-3}{2}}}\\= y^{ \frac{1}{4} - (\frac{-3}{2}) }= y^{\frac{7}{4}}\\=\sqrt[4]{ y^{7} }=|y|.\sqrt[4]{ y^{3} }\\---------------\)
11. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-2}{3} - \frac{2}{3} }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
12. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{2}{3} - (\frac{-4}{5}) }= a^{\frac{22}{15}}\\=\sqrt[15]{ a^{22} }=a.\sqrt[15]{ a^{7} }\\---------------\)