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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{1}{2}}}\\= x^{ \frac{1}{3} - \frac{1}{2} }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
2. \(\dfrac{y^{1}}{y^{\frac{1}{5}}}\\= y^{ 1 - \frac{1}{5} }= y^{\frac{4}{5}}\\=\sqrt[5]{ y^{4} }\\---------------\)
3. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{-5}{6}}}\\= x^{ \frac{3}{5} - (\frac{-5}{6}) }= x^{\frac{43}{30}}\\=\sqrt[30]{ x^{43} }=|x|.\sqrt[30]{ x^{13} }\\---------------\)
4. \(\dfrac{q^{2}}{q^{\frac{3}{5}}}\\= q^{ 2 - \frac{3}{5} }= q^{\frac{7}{5}}\\=\sqrt[5]{ q^{7} }=q.\sqrt[5]{ q^{2} }\\---------------\)
5. \(\dfrac{x^{\frac{-3}{4}}}{x^{\frac{3}{5}}}\\= x^{ \frac{-3}{4} - \frac{3}{5} }= x^{\frac{-27}{20}}\\=\frac{1}{\sqrt[20]{ x^{27} }}\\=\frac{1}{|x|.\sqrt[20]{ x^{7} }}=\frac{1}{|x|.\sqrt[20]{ x^{7} }} \color{purple}{\frac{\sqrt[20]{ x^{13} }}{\sqrt[20]{ x^{13} }}} \\=\frac{\sqrt[20]{ x^{13} }}{|x^{2}|}\\---------------\)
6. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-1}{3} - \frac{1}{3} }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
7. \(\dfrac{q^{-1}}{q^{\frac{5}{3}}}\\= q^{ -1 - \frac{5}{3} }= q^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ q^{8} }}\\=\frac{1}{q^{2}.\sqrt[3]{ q^{2} }}=\frac{1}{q^{2}.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{3}}\\---------------\)
8. \(\dfrac{y^{-2}}{y^{\frac{3}{5}}}\\= y^{ -2 - \frac{3}{5} }= y^{\frac{-13}{5}}\\=\frac{1}{\sqrt[5]{ y^{13} }}\\=\frac{1}{y^{2}.\sqrt[5]{ y^{3} }}=\frac{1}{y^{2}.\sqrt[5]{ y^{3} }} \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y^{3}}\\---------------\)
9. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{-2}{3} - (\frac{-2}{3}) }= a^{0}\\=1\\---------------\)
10. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{2}{3} - (\frac{-1}{3}) }= q^{1}\\\\---------------\)
11. \(\dfrac{y^{2}}{y^{\frac{1}{5}}}\\= y^{ 2 - \frac{1}{5} }= y^{\frac{9}{5}}\\=\sqrt[5]{ y^{9} }=y.\sqrt[5]{ y^{4} }\\---------------\)
12. \(\dfrac{q^{\frac{-4}{3}}}{q^{1}}\\= q^{ \frac{-4}{3} - 1 }= q^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ q^{7} }}\\=\frac{1}{q^{2}.\sqrt[3]{ q }}=\frac{1}{q^{2}.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{3}}\\---------------\)