Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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