Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{1}{2}}}\\= y^{ \frac{3}{4} - \frac{1}{2} }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
2. \(\dfrac{x^{-1}}{x^{\frac{-4}{5}}}\\= x^{ -1 - (\frac{-4}{5}) }= x^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ x }}=\frac{1}{\sqrt[5]{ x }}. \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x}\\---------------\)
3. \(\dfrac{q^{-2}}{q^{\frac{-5}{4}}}\\= q^{ -2 - (\frac{-5}{4}) }= q^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ q^{3} }}=\frac{1}{\sqrt[4]{ q^{3} }}. \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q|}\\---------------\)
4. \(\dfrac{q^{\frac{-1}{4}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{-1}{4} - (\frac{-5}{3}) }= q^{\frac{17}{12}}\\=\sqrt[12]{ q^{17} }=|q|.\sqrt[12]{ q^{5} }\\---------------\)
5. \(\dfrac{y^{\frac{-1}{3}}}{y^{1}}\\= y^{ \frac{-1}{3} - 1 }= y^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ y^{4} }}\\=\frac{1}{y.\sqrt[3]{ y }}=\frac{1}{y.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{2}}\\---------------\)
6. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{5}{3} - (\frac{-1}{2}) }= x^{\frac{13}{6}}\\=\sqrt[6]{ x^{13} }=|x^{2}|.\sqrt[6]{ x }\\---------------\)
7. \(\dfrac{x^{-1}}{x^{1}}\\= x^{ -1 - 1 }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
8. \(\dfrac{y^{\frac{-3}{2}}}{y^{\frac{3}{5}}}\\= y^{ \frac{-3}{2} - \frac{3}{5} }= y^{\frac{-21}{10}}\\=\frac{1}{\sqrt[10]{ y^{21} }}\\=\frac{1}{|y^{2}|.\sqrt[10]{ y }}=\frac{1}{|y^{2}|.\sqrt[10]{ y }} \color{purple}{\frac{\sqrt[10]{ y^{9} }}{\sqrt[10]{ y^{9} }}} \\=\frac{\sqrt[10]{ y^{9} }}{|y^{3}|}\\---------------\)
9. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{3}{2}}}\\= a^{ \frac{1}{2} - \frac{3}{2} }= a^{-1}\\=\frac{1}{a}\\---------------\)
10. \(\dfrac{x^{-1}}{x^{2}}\\= x^{ -1 - 2 }= x^{-3}\\=\frac{1}{x^{3}}\\---------------\)
11. \(\dfrac{y^{\frac{-1}{3}}}{y^{-1}}\\= y^{ \frac{-1}{3} - (-1) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
12. \(\dfrac{a^{\frac{1}{5}}}{a^{\frac{-5}{2}}}\\= a^{ \frac{1}{5} - (\frac{-5}{2}) }= a^{\frac{27}{10}}\\=\sqrt[10]{ a^{27} }=|a^{2}|.\sqrt[10]{ a^{7} }\\---------------\)