Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{-1}}{a^{\frac{-3}{5}}}\\= a^{ -1 - (\frac{-3}{5}) }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
2. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{2}{3}}}\\= y^{ \frac{1}{3} - \frac{2}{3} }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
3. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{3}{4}}}\\= a^{ \frac{1}{3} - \frac{3}{4} }= a^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ a^{5} }}=\frac{1}{\sqrt[12]{ a^{5} }}. \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a|}\\---------------\)
4. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{4}{5}}}\\= x^{ \frac{-1}{4} - \frac{4}{5} }= x^{\frac{-21}{20}}\\=\frac{1}{\sqrt[20]{ x^{21} }}\\=\frac{1}{|x|.\sqrt[20]{ x }}=\frac{1}{|x|.\sqrt[20]{ x }} \color{purple}{\frac{\sqrt[20]{ x^{19} }}{\sqrt[20]{ x^{19} }}} \\=\frac{\sqrt[20]{ x^{19} }}{|x^{2}|}\\---------------\)
5. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{-3}{2}}}\\= x^{ \frac{-2}{3} - (\frac{-3}{2}) }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
6. \(\dfrac{a^{\frac{-1}{4}}}{a^{1}}\\= a^{ \frac{-1}{4} - 1 }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
7. \(\dfrac{x^{\frac{2}{3}}}{x^{-1}}\\= x^{ \frac{2}{3} - (-1) }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)
8. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{5}{4}}}\\= x^{ \frac{-5}{3} - \frac{5}{4} }= x^{\frac{-35}{12}}\\=\frac{1}{\sqrt[12]{ x^{35} }}\\=\frac{1}{|x^{2}|.\sqrt[12]{ x^{11} }}=\frac{1}{|x^{2}|.\sqrt[12]{ x^{11} }} \color{purple}{\frac{\sqrt[12]{ x }}{\sqrt[12]{ x }}} \\=\frac{\sqrt[12]{ x }}{|x^{3}|}\\---------------\)
9. \(\dfrac{a^{\frac{-3}{2}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{-3}{2} - (\frac{-3}{5}) }= a^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ a^{9} }}=\frac{1}{\sqrt[10]{ a^{9} }}. \color{purple}{\frac{\sqrt[10]{ a }}{\sqrt[10]{ a }}} \\=\frac{\sqrt[10]{ a }}{|a|}\\---------------\)
10. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{3}{2}}}\\= x^{ \frac{1}{2} - \frac{3}{2} }= x^{-1}\\=\frac{1}{x}\\---------------\)
11. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{3}{2}}}\\= a^{ \frac{-2}{3} - \frac{3}{2} }= a^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ a^{13} }}\\=\frac{1}{|a^{2}|.\sqrt[6]{ a }}=\frac{1}{|a^{2}|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{3}|}\\---------------\)
12. \(\dfrac{a^{1}}{a^{-1}}\\= a^{ 1 - (-1) }= a^{2}\\\\---------------\)