Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{2}{3}}}{a^{1}}\\= a^{ \frac{2}{3} - 1 }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
2. \(\dfrac{a^{\frac{-4}{3}}}{a^{1}}\\= a^{ \frac{-4}{3} - 1 }= a^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ a^{7} }}\\=\frac{1}{a^{2}.\sqrt[3]{ a }}=\frac{1}{a^{2}.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{3}}\\---------------\)
3. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{5}{4}}}\\= x^{ \frac{3}{2} - \frac{5}{4} }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
4. \(\dfrac{y^{\frac{5}{6}}}{y^{-2}}\\= y^{ \frac{5}{6} - (-2) }= y^{\frac{17}{6}}\\=\sqrt[6]{ y^{17} }=|y^{2}|.\sqrt[6]{ y^{5} }\\---------------\)
5. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{-4}{5} - (\frac{-4}{3}) }= y^{\frac{8}{15}}\\=\sqrt[15]{ y^{8} }\\---------------\)
6. \(\dfrac{x^{\frac{5}{2}}}{x^{\frac{-4}{5}}}\\= x^{ \frac{5}{2} - (\frac{-4}{5}) }= x^{\frac{33}{10}}\\=\sqrt[10]{ x^{33} }=|x^{3}|.\sqrt[10]{ x^{3} }\\---------------\)
7. \(\dfrac{y^{\frac{3}{5}}}{y^{1}}\\= y^{ \frac{3}{5} - 1 }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)
8. \(\dfrac{q^{\frac{5}{2}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{5}{2} - (\frac{-1}{5}) }= q^{\frac{27}{10}}\\=\sqrt[10]{ q^{27} }=|q^{2}|.\sqrt[10]{ q^{7} }\\---------------\)
9. \(\dfrac{y^{1}}{y^{\frac{1}{5}}}\\= y^{ 1 - \frac{1}{5} }= y^{\frac{4}{5}}\\=\sqrt[5]{ y^{4} }\\---------------\)
10. \(\dfrac{q^{\frac{5}{4}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{5}{4} - (\frac{-1}{5}) }= q^{\frac{29}{20}}\\=\sqrt[20]{ q^{29} }=|q|.\sqrt[20]{ q^{9} }\\---------------\)
11. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{1}{3}}}\\= q^{ \frac{5}{3} - \frac{1}{3} }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
12. \(\dfrac{x^{\frac{1}{6}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{1}{6} - (\frac{-5}{4}) }= x^{\frac{17}{12}}\\=\sqrt[12]{ x^{17} }=|x|.\sqrt[12]{ x^{5} }\\---------------\)