Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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