Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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