Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{-1}}{q^{\frac{4}{5}}}\\= q^{ -1 - \frac{4}{5} }= q^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ q^{9} }}\\=\frac{1}{q.\sqrt[5]{ q^{4} }}=\frac{1}{q.\sqrt[5]{ q^{4} }} \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q^{2}}\\---------------\)
2. \(\dfrac{a^{-2}}{a^{\frac{1}{4}}}\\= a^{ -2 - \frac{1}{4} }= a^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ a^{9} }}\\=\frac{1}{|a^{2}|.\sqrt[4]{ a }}=\frac{1}{|a^{2}|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{3}|}\\---------------\)
3. \(\dfrac{x^{\frac{-2}{3}}}{x^{-1}}\\= x^{ \frac{-2}{3} - (-1) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
4. \(\dfrac{x^{-1}}{x^{\frac{5}{6}}}\\= x^{ -1 - \frac{5}{6} }= x^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ x^{11} }}\\=\frac{1}{|x|.\sqrt[6]{ x^{5} }}=\frac{1}{|x|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{2}|}\\---------------\)
5. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{4}{5}}}\\= y^{ \frac{-5}{4} - \frac{4}{5} }= y^{\frac{-41}{20}}\\=\frac{1}{\sqrt[20]{ y^{41} }}\\=\frac{1}{|y^{2}|.\sqrt[20]{ y }}=\frac{1}{|y^{2}|.\sqrt[20]{ y }} \color{purple}{\frac{\sqrt[20]{ y^{19} }}{\sqrt[20]{ y^{19} }}} \\=\frac{\sqrt[20]{ y^{19} }}{|y^{3}|}\\---------------\)
6. \(\dfrac{a^{-1}}{a^{\frac{2}{3}}}\\= a^{ -1 - \frac{2}{3} }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
7. \(\dfrac{x^{\frac{-3}{2}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-3}{2} - \frac{2}{3} }= x^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ x^{13} }}\\=\frac{1}{|x^{2}|.\sqrt[6]{ x }}=\frac{1}{|x^{2}|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{3}|}\\---------------\)
8. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-4}{3} - \frac{2}{3} }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
9. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-3}{4}}}\\= a^{ \frac{-1}{2} - (\frac{-3}{4}) }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
10. \(\dfrac{y^{\frac{-2}{5}}}{y^{-1}}\\= y^{ \frac{-2}{5} - (-1) }= y^{\frac{3}{5}}\\=\sqrt[5]{ y^{3} }\\---------------\)
11. \(\dfrac{x^{1}}{x^{\frac{-4}{5}}}\\= x^{ 1 - (\frac{-4}{5}) }= x^{\frac{9}{5}}\\=\sqrt[5]{ x^{9} }=x.\sqrt[5]{ x^{4} }\\---------------\)
12. \(\dfrac{y^{-2}}{y^{\frac{-3}{2}}}\\= y^{ -2 - (\frac{-3}{2}) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)