Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{1}}{y^{\frac{-3}{2}}}\\= y^{ 1 - (\frac{-3}{2}) }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)
2. \(\dfrac{a^{-2}}{a^{\frac{-1}{5}}}\\= a^{ -2 - (\frac{-1}{5}) }= a^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ a^{9} }}\\=\frac{1}{a.\sqrt[5]{ a^{4} }}=\frac{1}{a.\sqrt[5]{ a^{4} }} \color{purple}{\frac{\sqrt[5]{ a }}{\sqrt[5]{ a }}} \\=\frac{\sqrt[5]{ a }}{a^{2}}\\---------------\)
3. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{-4}{3} - (\frac{-3}{5}) }= x^{\frac{-11}{15}}\\=\frac{1}{\sqrt[15]{ x^{11} }}=\frac{1}{\sqrt[15]{ x^{11} }}. \color{purple}{\frac{\sqrt[15]{ x^{4} }}{\sqrt[15]{ x^{4} }}} \\=\frac{\sqrt[15]{ x^{4} }}{x}\\---------------\)
4. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-5}{2} - (\frac{-1}{3}) }= q^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ q^{13} }}\\=\frac{1}{|q^{2}|.\sqrt[6]{ q }}=\frac{1}{|q^{2}|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{3}|}\\---------------\)
5. \(\dfrac{x^{\frac{-3}{4}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-3}{4} - \frac{1}{2} }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
6. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{2}{5} - (\frac{-1}{2}) }= y^{\frac{9}{10}}\\=\sqrt[10]{ y^{9} }\\---------------\)
7. \(\dfrac{x^{\frac{4}{3}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{4}{3} - (\frac{-1}{2}) }= x^{\frac{11}{6}}\\=\sqrt[6]{ x^{11} }=|x|.\sqrt[6]{ x^{5} }\\---------------\)
8. \(\dfrac{x^{\frac{1}{4}}}{x^{1}}\\= x^{ \frac{1}{4} - 1 }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
9. \(\dfrac{x^{\frac{4}{3}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{4}{3} - (\frac{-5}{4}) }= x^{\frac{31}{12}}\\=\sqrt[12]{ x^{31} }=|x^{2}|.\sqrt[12]{ x^{7} }\\---------------\)
10. \(\dfrac{y^{\frac{1}{6}}}{y^{\frac{4}{5}}}\\= y^{ \frac{1}{6} - \frac{4}{5} }= y^{\frac{-19}{30}}\\=\frac{1}{\sqrt[30]{ y^{19} }}=\frac{1}{\sqrt[30]{ y^{19} }}. \color{purple}{\frac{\sqrt[30]{ y^{11} }}{\sqrt[30]{ y^{11} }}} \\=\frac{\sqrt[30]{ y^{11} }}{|y|}\\---------------\)
11. \(\dfrac{y^{-2}}{y^{\frac{-1}{3}}}\\= y^{ -2 - (\frac{-1}{3}) }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
12. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{-1}{3} - (\frac{-1}{5}) }= q^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ q^{2} }}=\frac{1}{\sqrt[15]{ q^{2} }}. \color{purple}{\frac{\sqrt[15]{ q^{13} }}{\sqrt[15]{ q^{13} }}} \\=\frac{\sqrt[15]{ q^{13} }}{q}\\---------------\)