Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{1}}{y^{\frac{-5}{3}}}\\= y^{ 1 - (\frac{-5}{3}) }= y^{\frac{8}{3}}\\=\sqrt[3]{ y^{8} }=y^{2}.\sqrt[3]{ y^{2} }\\---------------\)
2. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{5}{4}}}\\= x^{ \frac{-4}{5} - \frac{5}{4} }= x^{\frac{-41}{20}}\\=\frac{1}{\sqrt[20]{ x^{41} }}\\=\frac{1}{|x^{2}|.\sqrt[20]{ x }}=\frac{1}{|x^{2}|.\sqrt[20]{ x }} \color{purple}{\frac{\sqrt[20]{ x^{19} }}{\sqrt[20]{ x^{19} }}} \\=\frac{\sqrt[20]{ x^{19} }}{|x^{3}|}\\---------------\)
3. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-1}{2} - \frac{1}{2} }= x^{-1}\\=\frac{1}{x}\\---------------\)
4. \(\dfrac{a^{\frac{1}{6}}}{a^{\frac{3}{2}}}\\= a^{ \frac{1}{6} - \frac{3}{2} }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
5. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{2}{3} - (\frac{-5}{2}) }= q^{\frac{19}{6}}\\=\sqrt[6]{ q^{19} }=|q^{3}|.\sqrt[6]{ q }\\---------------\)
6. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{4}{3}}}\\= q^{ \frac{-1}{2} - \frac{4}{3} }= q^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ q^{11} }}\\=\frac{1}{|q|.\sqrt[6]{ q^{5} }}=\frac{1}{|q|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{2}|}\\---------------\)
7. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{1}{3} - (\frac{-4}{5}) }= q^{\frac{17}{15}}\\=\sqrt[15]{ q^{17} }=q.\sqrt[15]{ q^{2} }\\---------------\)
8. \(\dfrac{a^{\frac{1}{5}}}{a^{2}}\\= a^{ \frac{1}{5} - 2 }= a^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ a^{9} }}\\=\frac{1}{a.\sqrt[5]{ a^{4} }}=\frac{1}{a.\sqrt[5]{ a^{4} }} \color{purple}{\frac{\sqrt[5]{ a }}{\sqrt[5]{ a }}} \\=\frac{\sqrt[5]{ a }}{a^{2}}\\---------------\)
9. \(\dfrac{a^{-1}}{a^{\frac{-4}{3}}}\\= a^{ -1 - (\frac{-4}{3}) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
10. \(\dfrac{a^{\frac{3}{2}}}{a^{\frac{-4}{3}}}\\= a^{ \frac{3}{2} - (\frac{-4}{3}) }= a^{\frac{17}{6}}\\=\sqrt[6]{ a^{17} }=|a^{2}|.\sqrt[6]{ a^{5} }\\---------------\)
11. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{3}{2}}}\\= a^{ \frac{1}{2} - \frac{3}{2} }= a^{-1}\\=\frac{1}{a}\\---------------\)
12. \(\dfrac{y^{\frac{3}{2}}}{y^{\frac{3}{5}}}\\= y^{ \frac{3}{2} - \frac{3}{5} }= y^{\frac{9}{10}}\\=\sqrt[10]{ y^{9} }\\---------------\)