Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{4}{5}}}{q^{1}}\\= q^{ \frac{4}{5} - 1 }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)
2. \(\dfrac{q^{\frac{4}{5}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{4}{5} - (\frac{-5}{2}) }= q^{\frac{33}{10}}\\=\sqrt[10]{ q^{33} }=|q^{3}|.\sqrt[10]{ q^{3} }\\---------------\)
3. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-3}{4} - (\frac{-1}{2}) }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
4. \(\dfrac{x^{\frac{-2}{3}}}{x^{1}}\\= x^{ \frac{-2}{3} - 1 }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
5. \(\dfrac{y^{-1}}{y^{\frac{4}{3}}}\\= y^{ -1 - \frac{4}{3} }= y^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ y^{7} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y }}=\frac{1}{y^{2}.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{3}}\\---------------\)
6. \(\dfrac{y^{\frac{-5}{3}}}{y^{1}}\\= y^{ \frac{-5}{3} - 1 }= y^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ y^{8} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }}=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{3}}\\---------------\)
7. \(\dfrac{a^{-1}}{a^{\frac{1}{3}}}\\= a^{ -1 - \frac{1}{3} }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
8. \(\dfrac{x^{\frac{5}{2}}}{x^{\frac{3}{4}}}\\= x^{ \frac{5}{2} - \frac{3}{4} }= x^{\frac{7}{4}}\\=\sqrt[4]{ x^{7} }=|x|.\sqrt[4]{ x^{3} }\\---------------\)
9. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{-1}{2} - (\frac{-4}{3}) }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
10. \(\dfrac{q^{\frac{5}{4}}}{q^{\frac{-3}{4}}}\\= q^{ \frac{5}{4} - (\frac{-3}{4}) }= q^{2}\\\\---------------\)
11. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{3}{2}}}\\= x^{ \frac{3}{4} - \frac{3}{2} }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
12. \(\dfrac{y^{2}}{y^{\frac{-1}{6}}}\\= y^{ 2 - (\frac{-1}{6}) }= y^{\frac{13}{6}}\\=\sqrt[6]{ y^{13} }=|y^{2}|.\sqrt[6]{ y }\\---------------\)