Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{1}{6}}}{y^{\frac{3}{5}}}\\= y^{ \frac{1}{6} - \frac{3}{5} }= y^{\frac{-13}{30}}\\=\frac{1}{\sqrt[30]{ y^{13} }}=\frac{1}{\sqrt[30]{ y^{13} }}. \color{purple}{\frac{\sqrt[30]{ y^{17} }}{\sqrt[30]{ y^{17} }}} \\=\frac{\sqrt[30]{ y^{17} }}{|y|}\\---------------\)
2. \(\dfrac{q^{1}}{q^{\frac{-1}{3}}}\\= q^{ 1 - (\frac{-1}{3}) }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
3. \(\dfrac{q^{\frac{3}{5}}}{q^{\frac{-5}{4}}}\\= q^{ \frac{3}{5} - (\frac{-5}{4}) }= q^{\frac{37}{20}}\\=\sqrt[20]{ q^{37} }=|q|.\sqrt[20]{ q^{17} }\\---------------\)
4. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{5}{2} - (\frac{-3}{5}) }= y^{\frac{31}{10}}\\=\sqrt[10]{ y^{31} }=|y^{3}|.\sqrt[10]{ y }\\---------------\)
5. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{4}{3}}}\\= y^{ \frac{1}{4} - \frac{4}{3} }= y^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ y^{13} }}\\=\frac{1}{|y|.\sqrt[12]{ y }}=\frac{1}{|y|.\sqrt[12]{ y }} \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y^{2}|}\\---------------\)
6. \(\dfrac{x^{\frac{-5}{6}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-5}{6} - \frac{1}{3} }= x^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[6]{ x }}=\frac{1}{|x|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{2}|}\\---------------\)
7. \(\dfrac{a^{\frac{-4}{5}}}{a^{\frac{4}{3}}}\\= a^{ \frac{-4}{5} - \frac{4}{3} }= a^{\frac{-32}{15}}\\=\frac{1}{\sqrt[15]{ a^{32} }}\\=\frac{1}{a^{2}.\sqrt[15]{ a^{2} }}=\frac{1}{a^{2}.\sqrt[15]{ a^{2} }} \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a^{3}}\\---------------\)
8. \(\dfrac{x^{1}}{x^{1}}\\= x^{ 1 - 1 }= x^{0}\\=1\\---------------\)
9. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{-1}{4}}}\\= x^{ \frac{3}{4} - (\frac{-1}{4}) }= x^{1}\\\\---------------\)
10. \(\dfrac{x^{\frac{-1}{2}}}{x^{-1}}\\= x^{ \frac{-1}{2} - (-1) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
11. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-3}{4}}}\\= q^{ \frac{-1}{2} - (\frac{-3}{4}) }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
12. \(\dfrac{x^{\frac{-3}{2}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{-3}{2} - (\frac{-3}{5}) }= x^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ x^{9} }}=\frac{1}{\sqrt[10]{ x^{9} }}. \color{purple}{\frac{\sqrt[10]{ x }}{\sqrt[10]{ x }}} \\=\frac{\sqrt[10]{ x }}{|x|}\\---------------\)