Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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