Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{5}{3}}}\\= y^{ \frac{1}{4} - \frac{5}{3} }= y^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ y^{17} }}\\=\frac{1}{|y|.\sqrt[12]{ y^{5} }}=\frac{1}{|y|.\sqrt[12]{ y^{5} }} \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y^{2}|}\\---------------\)
2. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{5}{2}}}\\= y^{ \frac{-1}{3} - \frac{5}{2} }= y^{\frac{-17}{6}}\\=\frac{1}{\sqrt[6]{ y^{17} }}\\=\frac{1}{|y^{2}|.\sqrt[6]{ y^{5} }}=\frac{1}{|y^{2}|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{3}|}\\---------------\)
3. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{3}{5}}}\\= x^{ \frac{1}{2} - \frac{3}{5} }= x^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ x }}=\frac{1}{\sqrt[10]{ x }}. \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x|}\\---------------\)
4. \(\dfrac{a^{\frac{-3}{2}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{-3}{2} - (\frac{-1}{6}) }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
5. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-5}{6}}}\\= x^{ \frac{-1}{2} - (\frac{-5}{6}) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
6. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{-1}{2} - (\frac{-1}{6}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
7. \(\dfrac{y^{2}}{y^{\frac{-2}{3}}}\\= y^{ 2 - (\frac{-2}{3}) }= y^{\frac{8}{3}}\\=\sqrt[3]{ y^{8} }=y^{2}.\sqrt[3]{ y^{2} }\\---------------\)
8. \(\dfrac{y^{\frac{3}{2}}}{y^{-1}}\\= y^{ \frac{3}{2} - (-1) }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)
9. \(\dfrac{q^{\frac{-5}{4}}}{q^{\frac{2}{3}}}\\= q^{ \frac{-5}{4} - \frac{2}{3} }= q^{\frac{-23}{12}}\\=\frac{1}{\sqrt[12]{ q^{23} }}\\=\frac{1}{|q|.\sqrt[12]{ q^{11} }}=\frac{1}{|q|.\sqrt[12]{ q^{11} }} \color{purple}{\frac{\sqrt[12]{ q }}{\sqrt[12]{ q }}} \\=\frac{\sqrt[12]{ q }}{|q^{2}|}\\---------------\)
10. \(\dfrac{y^{1}}{y^{\frac{1}{4}}}\\= y^{ 1 - \frac{1}{4} }= y^{\frac{3}{4}}\\=\sqrt[4]{ y^{3} }\\---------------\)
11. \(\dfrac{q^{\frac{5}{2}}}{q^{\frac{-3}{5}}}\\= q^{ \frac{5}{2} - (\frac{-3}{5}) }= q^{\frac{31}{10}}\\=\sqrt[10]{ q^{31} }=|q^{3}|.\sqrt[10]{ q }\\---------------\)
12. \(\dfrac{q^{-1}}{q^{\frac{-1}{3}}}\\= q^{ -1 - (\frac{-1}{3}) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)