Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-5}{6}}}{q^{\frac{4}{3}}}\\= q^{ \frac{-5}{6} - \frac{4}{3} }= q^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ q^{13} }}\\=\frac{1}{|q^{2}|.\sqrt[6]{ q }}=\frac{1}{|q^{2}|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{3}|}\\---------------\)
2. \(\dfrac{a^{\frac{-3}{2}}}{a^{\frac{1}{4}}}\\= a^{ \frac{-3}{2} - \frac{1}{4} }= a^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[4]{ a^{3} }}=\frac{1}{|a|.\sqrt[4]{ a^{3} }} \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a^{2}|}\\---------------\)
3. \(\dfrac{q^{-1}}{q^{\frac{3}{4}}}\\= q^{ -1 - \frac{3}{4} }= q^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[4]{ q^{3} }}=\frac{1}{|q|.\sqrt[4]{ q^{3} }} \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q^{2}|}\\---------------\)
4. \(\dfrac{y^{\frac{4}{5}}}{y^{\frac{-5}{3}}}\\= y^{ \frac{4}{5} - (\frac{-5}{3}) }= y^{\frac{37}{15}}\\=\sqrt[15]{ y^{37} }=y^{2}.\sqrt[15]{ y^{7} }\\---------------\)
5. \(\dfrac{q^{\frac{2}{3}}}{q^{-1}}\\= q^{ \frac{2}{3} - (-1) }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
6. \(\dfrac{x^{\frac{-3}{2}}}{x^{\frac{-1}{5}}}\\= x^{ \frac{-3}{2} - (\frac{-1}{5}) }= x^{\frac{-13}{10}}\\=\frac{1}{\sqrt[10]{ x^{13} }}\\=\frac{1}{|x|.\sqrt[10]{ x^{3} }}=\frac{1}{|x|.\sqrt[10]{ x^{3} }} \color{purple}{\frac{\sqrt[10]{ x^{7} }}{\sqrt[10]{ x^{7} }}} \\=\frac{\sqrt[10]{ x^{7} }}{|x^{2}|}\\---------------\)
7. \(\dfrac{a^{\frac{-3}{4}}}{a^{-1}}\\= a^{ \frac{-3}{4} - (-1) }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
8. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-1}{3} - \frac{1}{3} }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
9. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{-3}{2}}}\\= a^{ \frac{1}{3} - (\frac{-3}{2}) }= a^{\frac{11}{6}}\\=\sqrt[6]{ a^{11} }=|a|.\sqrt[6]{ a^{5} }\\---------------\)
10. \(\dfrac{a^{-1}}{a^{2}}\\= a^{ -1 - 2 }= a^{-3}\\=\frac{1}{a^{3}}\\---------------\)
11. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{5}{6}}}\\= y^{ \frac{-3}{4} - \frac{5}{6} }= y^{\frac{-19}{12}}\\=\frac{1}{\sqrt[12]{ y^{19} }}\\=\frac{1}{|y|.\sqrt[12]{ y^{7} }}=\frac{1}{|y|.\sqrt[12]{ y^{7} }} \color{purple}{\frac{\sqrt[12]{ y^{5} }}{\sqrt[12]{ y^{5} }}} \\=\frac{\sqrt[12]{ y^{5} }}{|y^{2}|}\\---------------\)
12. \(\dfrac{x^{\frac{1}{4}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{1}{4} - (\frac{-1}{2}) }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)