Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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