Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{1}{2}}}{y^{-1}}\\= y^{ \frac{1}{2} - (-1) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
2. \(\dfrac{y^{\frac{4}{5}}}{y^{\frac{5}{2}}}\\= y^{ \frac{4}{5} - \frac{5}{2} }= y^{\frac{-17}{10}}\\=\frac{1}{\sqrt[10]{ y^{17} }}\\=\frac{1}{|y|.\sqrt[10]{ y^{7} }}=\frac{1}{|y|.\sqrt[10]{ y^{7} }} \color{purple}{\frac{\sqrt[10]{ y^{3} }}{\sqrt[10]{ y^{3} }}} \\=\frac{\sqrt[10]{ y^{3} }}{|y^{2}|}\\---------------\)
3. \(\dfrac{a^{\frac{5}{4}}}{a^{\frac{3}{5}}}\\= a^{ \frac{5}{4} - \frac{3}{5} }= a^{\frac{13}{20}}\\=\sqrt[20]{ a^{13} }\\---------------\)
4. \(\dfrac{q^{\frac{1}{5}}}{q^{\frac{1}{3}}}\\= q^{ \frac{1}{5} - \frac{1}{3} }= q^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ q^{2} }}=\frac{1}{\sqrt[15]{ q^{2} }}. \color{purple}{\frac{\sqrt[15]{ q^{13} }}{\sqrt[15]{ q^{13} }}} \\=\frac{\sqrt[15]{ q^{13} }}{q}\\---------------\)
5. \(\dfrac{x^{-1}}{x^{\frac{-2}{5}}}\\= x^{ -1 - (\frac{-2}{5}) }= x^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ x^{3} }}=\frac{1}{\sqrt[5]{ x^{3} }}. \color{purple}{\frac{\sqrt[5]{ x^{2} }}{\sqrt[5]{ x^{2} }}} \\=\frac{\sqrt[5]{ x^{2} }}{x}\\---------------\)
6. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-5}{2}}}\\= a^{ \frac{1}{2} - (\frac{-5}{2}) }= a^{3}\\\\---------------\)
7. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{4}{3} - (\frac{-5}{2}) }= y^{\frac{23}{6}}\\=\sqrt[6]{ y^{23} }=|y^{3}|.\sqrt[6]{ y^{5} }\\---------------\)
8. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{-1}{4}}}\\= y^{ \frac{2}{3} - (\frac{-1}{4}) }= y^{\frac{11}{12}}\\=\sqrt[12]{ y^{11} }\\---------------\)
9. \(\dfrac{x^{\frac{-5}{3}}}{x^{2}}\\= x^{ \frac{-5}{3} - 2 }= x^{\frac{-11}{3}}\\=\frac{1}{\sqrt[3]{ x^{11} }}\\=\frac{1}{x^{3}.\sqrt[3]{ x^{2} }}=\frac{1}{x^{3}.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{4}}\\---------------\)
10. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{1}{5}}}\\= x^{ \frac{-1}{3} - \frac{1}{5} }= x^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ x^{8} }}=\frac{1}{\sqrt[15]{ x^{8} }}. \color{purple}{\frac{\sqrt[15]{ x^{7} }}{\sqrt[15]{ x^{7} }}} \\=\frac{\sqrt[15]{ x^{7} }}{x}\\---------------\)
11. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-2}{3} - \frac{1}{3} }= x^{-1}\\=\frac{1}{x}\\---------------\)
12. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-1}{4}}}\\= a^{ \frac{-1}{2} - (\frac{-1}{4}) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)