Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{4}{3} - (\frac{-3}{5}) }= y^{\frac{29}{15}}\\=\sqrt[15]{ y^{29} }=y.\sqrt[15]{ y^{14} }\\---------------\)
2. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{5}{4}}}\\= a^{ \frac{-2}{3} - \frac{5}{4} }= a^{\frac{-23}{12}}\\=\frac{1}{\sqrt[12]{ a^{23} }}\\=\frac{1}{|a|.\sqrt[12]{ a^{11} }}=\frac{1}{|a|.\sqrt[12]{ a^{11} }} \color{purple}{\frac{\sqrt[12]{ a }}{\sqrt[12]{ a }}} \\=\frac{\sqrt[12]{ a }}{|a^{2}|}\\---------------\)
3. \(\dfrac{q^{1}}{q^{2}}\\= q^{ 1 - 2 }= q^{-1}\\=\frac{1}{q}\\---------------\)
4. \(\dfrac{x^{2}}{x^{\frac{1}{6}}}\\= x^{ 2 - \frac{1}{6} }= x^{\frac{11}{6}}\\=\sqrt[6]{ x^{11} }=|x|.\sqrt[6]{ x^{5} }\\---------------\)
5. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-5}{6} - (\frac{-1}{3}) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
6. \(\dfrac{a^{\frac{-2}{5}}}{a^{\frac{3}{4}}}\\= a^{ \frac{-2}{5} - \frac{3}{4} }= a^{\frac{-23}{20}}\\=\frac{1}{\sqrt[20]{ a^{23} }}\\=\frac{1}{|a|.\sqrt[20]{ a^{3} }}=\frac{1}{|a|.\sqrt[20]{ a^{3} }} \color{purple}{\frac{\sqrt[20]{ a^{17} }}{\sqrt[20]{ a^{17} }}} \\=\frac{\sqrt[20]{ a^{17} }}{|a^{2}|}\\---------------\)
7. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{3}{4}}}\\= y^{ \frac{1}{3} - \frac{3}{4} }= y^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ y^{5} }}=\frac{1}{\sqrt[12]{ y^{5} }}. \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y|}\\---------------\)
8. \(\dfrac{y^{\frac{-4}{3}}}{y^{2}}\\= y^{ \frac{-4}{3} - 2 }= y^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ y^{10} }}\\=\frac{1}{y^{3}.\sqrt[3]{ y }}=\frac{1}{y^{3}.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{4}}\\---------------\)
9. \(\dfrac{y^{\frac{1}{3}}}{y^{1}}\\= y^{ \frac{1}{3} - 1 }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
10. \(\dfrac{x^{\frac{5}{2}}}{x^{1}}\\= x^{ \frac{5}{2} - 1 }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
11. \(\dfrac{x^{\frac{-5}{6}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{-5}{6} - (\frac{-2}{3}) }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
12. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{-3}{4} - (\frac{-4}{5}) }= q^{\frac{1}{20}}\\=\sqrt[20]{ q }\\---------------\)