Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{-3}{4}}}\\= y^{ \frac{5}{2} - (\frac{-3}{4}) }= y^{\frac{13}{4}}\\=\sqrt[4]{ y^{13} }=|y^{3}|.\sqrt[4]{ y }\\---------------\)
2. \(\dfrac{a^{\frac{2}{3}}}{a^{2}}\\= a^{ \frac{2}{3} - 2 }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
3. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{1}{3}}}\\= a^{ \frac{2}{5} - \frac{1}{3} }= a^{\frac{1}{15}}\\=\sqrt[15]{ a }\\---------------\)
4. \(\dfrac{x^{\frac{2}{5}}}{x^{\frac{-5}{2}}}\\= x^{ \frac{2}{5} - (\frac{-5}{2}) }= x^{\frac{29}{10}}\\=\sqrt[10]{ x^{29} }=|x^{2}|.\sqrt[10]{ x^{9} }\\---------------\)
5. \(\dfrac{y^{1}}{y^{\frac{-5}{4}}}\\= y^{ 1 - (\frac{-5}{4}) }= y^{\frac{9}{4}}\\=\sqrt[4]{ y^{9} }=|y^{2}|.\sqrt[4]{ y }\\---------------\)
6. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-5}{4} - \frac{1}{3} }= y^{\frac{-19}{12}}\\=\frac{1}{\sqrt[12]{ y^{19} }}\\=\frac{1}{|y|.\sqrt[12]{ y^{7} }}=\frac{1}{|y|.\sqrt[12]{ y^{7} }} \color{purple}{\frac{\sqrt[12]{ y^{5} }}{\sqrt[12]{ y^{5} }}} \\=\frac{\sqrt[12]{ y^{5} }}{|y^{2}|}\\---------------\)
7. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-5}{6}}}\\= x^{ \frac{-1}{2} - (\frac{-5}{6}) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
8. \(\dfrac{x^{\frac{5}{6}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{5}{6} - (\frac{-1}{2}) }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)
9. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{1}{3}}}\\= x^{ \frac{3}{4} - \frac{1}{3} }= x^{\frac{5}{12}}\\=\sqrt[12]{ x^{5} }\\---------------\)
10. \(\dfrac{x^{\frac{3}{2}}}{x^{-2}}\\= x^{ \frac{3}{2} - (-2) }= x^{\frac{7}{2}}\\= \sqrt{ x^{7} } =|x^{3}|. \sqrt{ x } \\---------------\)
11. \(\dfrac{x^{-1}}{x^{\frac{5}{4}}}\\= x^{ -1 - \frac{5}{4} }= x^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ x^{9} }}\\=\frac{1}{|x^{2}|.\sqrt[4]{ x }}=\frac{1}{|x^{2}|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{3}|}\\---------------\)
12. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{2}{3}}}\\= q^{ \frac{-2}{3} - \frac{2}{3} }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)