Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-5}{2}}}{a^{\frac{-1}{5}}}\\= a^{ \frac{-5}{2} - (\frac{-1}{5}) }= a^{\frac{-23}{10}}\\=\frac{1}{\sqrt[10]{ a^{23} }}\\=\frac{1}{|a^{2}|.\sqrt[10]{ a^{3} }}=\frac{1}{|a^{2}|.\sqrt[10]{ a^{3} }} \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a^{3}|}\\---------------\)
2. \(\dfrac{a^{\frac{-1}{3}}}{a^{-1}}\\= a^{ \frac{-1}{3} - (-1) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
3. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{-1}{2} - (\frac{-5}{3}) }= q^{\frac{7}{6}}\\=\sqrt[6]{ q^{7} }=|q|.\sqrt[6]{ q }\\---------------\)
4. \(\dfrac{a^{\frac{-3}{5}}}{a^{\frac{-3}{2}}}\\= a^{ \frac{-3}{5} - (\frac{-3}{2}) }= a^{\frac{9}{10}}\\=\sqrt[10]{ a^{9} }\\---------------\)
5. \(\dfrac{y^{\frac{-1}{4}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-1}{4} - \frac{1}{2} }= y^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ y^{3} }}=\frac{1}{\sqrt[4]{ y^{3} }}. \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y|}\\---------------\)
6. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{3}{4}}}\\= x^{ \frac{-2}{3} - \frac{3}{4} }= x^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ x^{17} }}\\=\frac{1}{|x|.\sqrt[12]{ x^{5} }}=\frac{1}{|x|.\sqrt[12]{ x^{5} }} \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x^{2}|}\\---------------\)
7. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{5}{6}}}\\= x^{ \frac{-1}{3} - \frac{5}{6} }= x^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[6]{ x }}=\frac{1}{|x|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{2}|}\\---------------\)
8. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{-3}{2}}}\\= y^{ \frac{3}{5} - (\frac{-3}{2}) }= y^{\frac{21}{10}}\\=\sqrt[10]{ y^{21} }=|y^{2}|.\sqrt[10]{ y }\\---------------\)
9. \(\dfrac{q^{-1}}{q^{\frac{2}{3}}}\\= q^{ -1 - \frac{2}{3} }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
10. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-1}{3} - \frac{2}{3} }= a^{-1}\\=\frac{1}{a}\\---------------\)
11. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-1}{3} - (\frac{-1}{2}) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
12. \(\dfrac{q^{\frac{5}{4}}}{q^{\frac{1}{2}}}\\= q^{ \frac{5}{4} - \frac{1}{2} }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)