Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{5}{3}}}{x^{2}}\\= x^{ \frac{5}{3} - 2 }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
2. \(\dfrac{y^{\frac{-3}{2}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-3}{2} - \frac{1}{2} }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
3. \(\dfrac{y^{1}}{y^{\frac{-2}{3}}}\\= y^{ 1 - (\frac{-2}{3}) }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
4. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{-5}{3}}}\\= a^{ \frac{4}{5} - (\frac{-5}{3}) }= a^{\frac{37}{15}}\\=\sqrt[15]{ a^{37} }=a^{2}.\sqrt[15]{ a^{7} }\\---------------\)
5. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{2}{3}}}\\= q^{ \frac{-3}{4} - \frac{2}{3} }= q^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ q^{17} }}\\=\frac{1}{|q|.\sqrt[12]{ q^{5} }}=\frac{1}{|q|.\sqrt[12]{ q^{5} }} \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q^{2}|}\\---------------\)
6. \(\dfrac{a^{\frac{5}{4}}}{a^{1}}\\= a^{ \frac{5}{4} - 1 }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
7. \(\dfrac{q^{1}}{q^{2}}\\= q^{ 1 - 2 }= q^{-1}\\=\frac{1}{q}\\---------------\)
8. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{1}{6}}}\\= q^{ \frac{1}{4} - \frac{1}{6} }= q^{\frac{1}{12}}\\=\sqrt[12]{ q }\\---------------\)
9. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-2}{3} - (\frac{-1}{3}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
10. \(\dfrac{q^{\frac{5}{2}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{5}{2} - (\frac{-5}{2}) }= q^{5}\\\\---------------\)
11. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-1}{2} - (\frac{-1}{2}) }= a^{0}\\=1\\---------------\)
12. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{5}{2}}}\\= x^{ \frac{-5}{3} - \frac{5}{2} }= x^{\frac{-25}{6}}\\=\frac{1}{\sqrt[6]{ x^{25} }}\\=\frac{1}{|x^{4}|.\sqrt[6]{ x }}=\frac{1}{|x^{4}|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{5}|}\\---------------\)