Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{1}{2} - (\frac{-1}{2}) }= y^{1}\\\\---------------\)
2. \(\dfrac{a^{-1}}{a^{2}}\\= a^{ -1 - 2 }= a^{-3}\\=\frac{1}{a^{3}}\\---------------\)
3. \(\dfrac{y^{\frac{3}{2}}}{y^{\frac{2}{3}}}\\= y^{ \frac{3}{2} - \frac{2}{3} }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
4. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-4}{3} - \frac{2}{3} }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
5. \(\dfrac{a^{1}}{a^{\frac{3}{5}}}\\= a^{ 1 - \frac{3}{5} }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
6. \(\dfrac{a^{\frac{-5}{4}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-5}{4} - (\frac{-1}{2}) }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
7. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{3}{5} - (\frac{-2}{3}) }= x^{\frac{19}{15}}\\=\sqrt[15]{ x^{19} }=x.\sqrt[15]{ x^{4} }\\---------------\)
8. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{3}{2} - (\frac{-1}{2}) }= x^{2}\\\\---------------\)
9. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-1}{3} - (\frac{-1}{2}) }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
10. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{5}{6}}}\\= y^{ \frac{-3}{5} - \frac{5}{6} }= y^{\frac{-43}{30}}\\=\frac{1}{\sqrt[30]{ y^{43} }}\\=\frac{1}{|y|.\sqrt[30]{ y^{13} }}=\frac{1}{|y|.\sqrt[30]{ y^{13} }} \color{purple}{\frac{\sqrt[30]{ y^{17} }}{\sqrt[30]{ y^{17} }}} \\=\frac{\sqrt[30]{ y^{17} }}{|y^{2}|}\\---------------\)
11. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{3}{4}}}\\= y^{ \frac{4}{3} - \frac{3}{4} }= y^{\frac{7}{12}}\\=\sqrt[12]{ y^{7} }\\---------------\)
12. \(\dfrac{a^{\frac{-4}{3}}}{a^{-1}}\\= a^{ \frac{-4}{3} - (-1) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)