Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{1}{6}}}{y^{\frac{-5}{4}}}\\= y^{ \frac{1}{6} - (\frac{-5}{4}) }= y^{\frac{17}{12}}\\=\sqrt[12]{ y^{17} }=|y|.\sqrt[12]{ y^{5} }\\---------------\)
2. \(\dfrac{a^{\frac{-4}{5}}}{a^{\frac{3}{4}}}\\= a^{ \frac{-4}{5} - \frac{3}{4} }= a^{\frac{-31}{20}}\\=\frac{1}{\sqrt[20]{ a^{31} }}\\=\frac{1}{|a|.\sqrt[20]{ a^{11} }}=\frac{1}{|a|.\sqrt[20]{ a^{11} }} \color{purple}{\frac{\sqrt[20]{ a^{9} }}{\sqrt[20]{ a^{9} }}} \\=\frac{\sqrt[20]{ a^{9} }}{|a^{2}|}\\---------------\)
3. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{5}{4}}}\\= q^{ \frac{-1}{3} - \frac{5}{4} }= q^{\frac{-19}{12}}\\=\frac{1}{\sqrt[12]{ q^{19} }}\\=\frac{1}{|q|.\sqrt[12]{ q^{7} }}=\frac{1}{|q|.\sqrt[12]{ q^{7} }} \color{purple}{\frac{\sqrt[12]{ q^{5} }}{\sqrt[12]{ q^{5} }}} \\=\frac{\sqrt[12]{ q^{5} }}{|q^{2}|}\\---------------\)
4. \(\dfrac{q^{\frac{5}{2}}}{q^{\frac{3}{4}}}\\= q^{ \frac{5}{2} - \frac{3}{4} }= q^{\frac{7}{4}}\\=\sqrt[4]{ q^{7} }=|q|.\sqrt[4]{ q^{3} }\\---------------\)
5. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{-3}{4} - (\frac{-2}{5}) }= y^{\frac{-7}{20}}\\=\frac{1}{\sqrt[20]{ y^{7} }}=\frac{1}{\sqrt[20]{ y^{7} }}. \color{purple}{\frac{\sqrt[20]{ y^{13} }}{\sqrt[20]{ y^{13} }}} \\=\frac{\sqrt[20]{ y^{13} }}{|y|}\\---------------\)
6. \(\dfrac{y^{\frac{-2}{5}}}{y^{-2}}\\= y^{ \frac{-2}{5} - (-2) }= y^{\frac{8}{5}}\\=\sqrt[5]{ y^{8} }=y.\sqrt[5]{ y^{3} }\\---------------\)
7. \(\dfrac{a^{\frac{-3}{2}}}{a^{\frac{3}{5}}}\\= a^{ \frac{-3}{2} - \frac{3}{5} }= a^{\frac{-21}{10}}\\=\frac{1}{\sqrt[10]{ a^{21} }}\\=\frac{1}{|a^{2}|.\sqrt[10]{ a }}=\frac{1}{|a^{2}|.\sqrt[10]{ a }} \color{purple}{\frac{\sqrt[10]{ a^{9} }}{\sqrt[10]{ a^{9} }}} \\=\frac{\sqrt[10]{ a^{9} }}{|a^{3}|}\\---------------\)
8. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{-1}{2} - (\frac{-2}{5}) }= y^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ y }}=\frac{1}{\sqrt[10]{ y }}. \color{purple}{\frac{\sqrt[10]{ y^{9} }}{\sqrt[10]{ y^{9} }}} \\=\frac{\sqrt[10]{ y^{9} }}{|y|}\\---------------\)
9. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-1}{3} - \frac{1}{3} }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
10. \(\dfrac{q^{\frac{-5}{4}}}{q^{\frac{5}{3}}}\\= q^{ \frac{-5}{4} - \frac{5}{3} }= q^{\frac{-35}{12}}\\=\frac{1}{\sqrt[12]{ q^{35} }}\\=\frac{1}{|q^{2}|.\sqrt[12]{ q^{11} }}=\frac{1}{|q^{2}|.\sqrt[12]{ q^{11} }} \color{purple}{\frac{\sqrt[12]{ q }}{\sqrt[12]{ q }}} \\=\frac{\sqrt[12]{ q }}{|q^{3}|}\\---------------\)
11. \(\dfrac{q^{-2}}{q^{\frac{5}{4}}}\\= q^{ -2 - \frac{5}{4} }= q^{\frac{-13}{4}}\\=\frac{1}{\sqrt[4]{ q^{13} }}\\=\frac{1}{|q^{3}|.\sqrt[4]{ q }}=\frac{1}{|q^{3}|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{4}|}\\---------------\)
12. \(\dfrac{x^{1}}{x^{\frac{1}{2}}}\\= x^{ 1 - \frac{1}{2} }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)