Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{-1}}{y^{\frac{-4}{5}}}\\= y^{ -1 - (\frac{-4}{5}) }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)
2. \(\dfrac{x^{2}}{x^{\frac{3}{2}}}\\= x^{ 2 - \frac{3}{2} }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
3. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{1}{5}}}\\= y^{ \frac{2}{5} - \frac{1}{5} }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)
4. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{2}{3}}}\\= q^{ \frac{2}{5} - \frac{2}{3} }= q^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ q^{4} }}=\frac{1}{\sqrt[15]{ q^{4} }}. \color{purple}{\frac{\sqrt[15]{ q^{11} }}{\sqrt[15]{ q^{11} }}} \\=\frac{\sqrt[15]{ q^{11} }}{q}\\---------------\)
5. \(\dfrac{x^{\frac{1}{5}}}{x^{-1}}\\= x^{ \frac{1}{5} - (-1) }= x^{\frac{6}{5}}\\=\sqrt[5]{ x^{6} }=x.\sqrt[5]{ x }\\---------------\)
6. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{5}{3} - (\frac{-1}{6}) }= q^{\frac{11}{6}}\\=\sqrt[6]{ q^{11} }=|q|.\sqrt[6]{ q^{5} }\\---------------\)
7. \(\dfrac{q^{-1}}{q^{\frac{3}{4}}}\\= q^{ -1 - \frac{3}{4} }= q^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[4]{ q^{3} }}=\frac{1}{|q|.\sqrt[4]{ q^{3} }} \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q^{2}|}\\---------------\)
8. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{5}{4}}}\\= y^{ \frac{-2}{3} - \frac{5}{4} }= y^{\frac{-23}{12}}\\=\frac{1}{\sqrt[12]{ y^{23} }}\\=\frac{1}{|y|.\sqrt[12]{ y^{11} }}=\frac{1}{|y|.\sqrt[12]{ y^{11} }} \color{purple}{\frac{\sqrt[12]{ y }}{\sqrt[12]{ y }}} \\=\frac{\sqrt[12]{ y }}{|y^{2}|}\\---------------\)
9. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{3}{4}}}\\= x^{ \frac{2}{3} - \frac{3}{4} }= x^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ x }}=\frac{1}{\sqrt[12]{ x }}. \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x|}\\---------------\)
10. \(\dfrac{a^{2}}{a^{\frac{4}{5}}}\\= a^{ 2 - \frac{4}{5} }= a^{\frac{6}{5}}\\=\sqrt[5]{ a^{6} }=a.\sqrt[5]{ a }\\---------------\)
11. \(\dfrac{y^{\frac{-3}{2}}}{y^{\frac{-1}{4}}}\\= y^{ \frac{-3}{2} - (\frac{-1}{4}) }= y^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ y^{5} }}\\=\frac{1}{|y|.\sqrt[4]{ y }}=\frac{1}{|y|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{2}|}\\---------------\)
12. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{-1}{2} - (\frac{-1}{3}) }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)