Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-5}{2}}}\\= a^{ \frac{2}{3} - (\frac{-5}{2}) }= a^{\frac{19}{6}}\\=\sqrt[6]{ a^{19} }=|a^{3}|.\sqrt[6]{ a }\\---------------\)
2. \(\dfrac{a^{\frac{-2}{5}}}{a^{\frac{1}{5}}}\\= a^{ \frac{-2}{5} - \frac{1}{5} }= a^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ a^{3} }}=\frac{1}{\sqrt[5]{ a^{3} }}. \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a}\\---------------\)
3. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{-1}{4}}}\\= x^{ \frac{-4}{3} - (\frac{-1}{4}) }= x^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ x^{13} }}\\=\frac{1}{|x|.\sqrt[12]{ x }}=\frac{1}{|x|.\sqrt[12]{ x }} \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x^{2}|}\\---------------\)
4. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{1}{3}}}\\= a^{ \frac{2}{3} - \frac{1}{3} }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
5. \(\dfrac{q^{\frac{3}{5}}}{q^{\frac{5}{3}}}\\= q^{ \frac{3}{5} - \frac{5}{3} }= q^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ q^{16} }}\\=\frac{1}{q.\sqrt[15]{ q }}=\frac{1}{q.\sqrt[15]{ q }} \color{purple}{\frac{\sqrt[15]{ q^{14} }}{\sqrt[15]{ q^{14} }}} \\=\frac{\sqrt[15]{ q^{14} }}{q^{2}}\\---------------\)
6. \(\dfrac{x^{\frac{2}{5}}}{x^{\frac{3}{5}}}\\= x^{ \frac{2}{5} - \frac{3}{5} }= x^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ x }}=\frac{1}{\sqrt[5]{ x }}. \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x}\\---------------\)
7. \(\dfrac{q^{\frac{3}{2}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{3}{2} - (\frac{-5}{3}) }= q^{\frac{19}{6}}\\=\sqrt[6]{ q^{19} }=|q^{3}|.\sqrt[6]{ q }\\---------------\)
8. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{-1}{2} - (\frac{-1}{3}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
9. \(\dfrac{x^{1}}{x^{\frac{1}{3}}}\\= x^{ 1 - \frac{1}{3} }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
10. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{-1}{3} - (\frac{-2}{5}) }= a^{\frac{1}{15}}\\=\sqrt[15]{ a }\\---------------\)
11. \(\dfrac{x^{1}}{x^{\frac{-1}{3}}}\\= x^{ 1 - (\frac{-1}{3}) }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)
12. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{-5}{3}}}\\= x^{ \frac{-5}{4} - (\frac{-5}{3}) }= x^{\frac{5}{12}}\\=\sqrt[12]{ x^{5} }\\---------------\)