Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-2}{3}}}{a^{1}}\\= a^{ \frac{-2}{3} - 1 }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
2. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{-3}{4}}}\\= a^{ \frac{-5}{6} - (\frac{-3}{4}) }= a^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ a }}=\frac{1}{\sqrt[12]{ a }}. \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a|}\\---------------\)
3. \(\dfrac{x^{\frac{1}{4}}}{x^{\frac{1}{2}}}\\= x^{ \frac{1}{4} - \frac{1}{2} }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
4. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{1}{4}}}\\= x^{ \frac{-1}{4} - \frac{1}{4} }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
5. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{3}{2}}}\\= a^{ \frac{1}{2} - \frac{3}{2} }= a^{-1}\\=\frac{1}{a}\\---------------\)
6. \(\dfrac{y^{-1}}{y^{\frac{-2}{3}}}\\= y^{ -1 - (\frac{-2}{3}) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
7. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{5}{6}}}\\= y^{ \frac{-5}{2} - \frac{5}{6} }= y^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ y^{10} }}\\=\frac{1}{y^{3}.\sqrt[3]{ y }}=\frac{1}{y^{3}.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{4}}\\---------------\)
8. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{3}{4}}}\\= a^{ \frac{-2}{3} - \frac{3}{4} }= a^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ a^{17} }}\\=\frac{1}{|a|.\sqrt[12]{ a^{5} }}=\frac{1}{|a|.\sqrt[12]{ a^{5} }} \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a^{2}|}\\---------------\)
9. \(\dfrac{a^{\frac{-1}{3}}}{a^{-1}}\\= a^{ \frac{-1}{3} - (-1) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
10. \(\dfrac{q^{1}}{q^{\frac{-4}{3}}}\\= q^{ 1 - (\frac{-4}{3}) }= q^{\frac{7}{3}}\\=\sqrt[3]{ q^{7} }=q^{2}.\sqrt[3]{ q }\\---------------\)
11. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{3}{5}}}\\= x^{ \frac{5}{3} - \frac{3}{5} }= x^{\frac{16}{15}}\\=\sqrt[15]{ x^{16} }=x.\sqrt[15]{ x }\\---------------\)
12. \(\dfrac{y^{-1}}{y^{\frac{1}{4}}}\\= y^{ -1 - \frac{1}{4} }= y^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ y^{5} }}\\=\frac{1}{|y|.\sqrt[4]{ y }}=\frac{1}{|y|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{2}|}\\---------------\)