Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-1}{3} - (\frac{-1}{2}) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
2. \(\dfrac{y^{\frac{-1}{4}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{-1}{4} - (\frac{-2}{5}) }= y^{\frac{3}{20}}\\=\sqrt[20]{ y^{3} }\\---------------\)
3. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{3}{5}}}\\= a^{ \frac{1}{2} - \frac{3}{5} }= a^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ a }}=\frac{1}{\sqrt[10]{ a }}. \color{purple}{\frac{\sqrt[10]{ a^{9} }}{\sqrt[10]{ a^{9} }}} \\=\frac{\sqrt[10]{ a^{9} }}{|a|}\\---------------\)
4. \(\dfrac{x^{\frac{1}{4}}}{x^{\frac{-1}{4}}}\\= x^{ \frac{1}{4} - (\frac{-1}{4}) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
5. \(\dfrac{a^{\frac{1}{5}}}{a^{\frac{5}{3}}}\\= a^{ \frac{1}{5} - \frac{5}{3} }= a^{\frac{-22}{15}}\\=\frac{1}{\sqrt[15]{ a^{22} }}\\=\frac{1}{a.\sqrt[15]{ a^{7} }}=\frac{1}{a.\sqrt[15]{ a^{7} }} \color{purple}{\frac{\sqrt[15]{ a^{8} }}{\sqrt[15]{ a^{8} }}} \\=\frac{\sqrt[15]{ a^{8} }}{a^{2}}\\---------------\)
6. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{-1}{2} - (\frac{-5}{2}) }= q^{2}\\\\---------------\)
7. \(\dfrac{x^{\frac{-3}{4}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-3}{4} - \frac{2}{3} }= x^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ x^{17} }}\\=\frac{1}{|x|.\sqrt[12]{ x^{5} }}=\frac{1}{|x|.\sqrt[12]{ x^{5} }} \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x^{2}|}\\---------------\)
8. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{1}{3} - (\frac{-2}{3}) }= q^{1}\\\\---------------\)
9. \(\dfrac{a^{\frac{-1}{4}}}{a^{-1}}\\= a^{ \frac{-1}{4} - (-1) }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
10. \(\dfrac{q^{\frac{-5}{3}}}{q^{\frac{1}{4}}}\\= q^{ \frac{-5}{3} - \frac{1}{4} }= q^{\frac{-23}{12}}\\=\frac{1}{\sqrt[12]{ q^{23} }}\\=\frac{1}{|q|.\sqrt[12]{ q^{11} }}=\frac{1}{|q|.\sqrt[12]{ q^{11} }} \color{purple}{\frac{\sqrt[12]{ q }}{\sqrt[12]{ q }}} \\=\frac{\sqrt[12]{ q }}{|q^{2}|}\\---------------\)
11. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{-3}{2}}}\\= q^{ \frac{5}{3} - (\frac{-3}{2}) }= q^{\frac{19}{6}}\\=\sqrt[6]{ q^{19} }=|q^{3}|.\sqrt[6]{ q }\\---------------\)
12. \(\dfrac{a^{1}}{a^{\frac{-1}{2}}}\\= a^{ 1 - (\frac{-1}{2}) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)