Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-3}{5}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{-3}{5} - (\frac{-3}{5}) }= a^{0}\\=1\\---------------\)
2. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{5}{4}}}\\= x^{ \frac{-1}{2} - \frac{5}{4} }= x^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[4]{ x^{3} }}=\frac{1}{|x|.\sqrt[4]{ x^{3} }} \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x^{2}|}\\---------------\)
3. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{4}{5}}}\\= y^{ \frac{1}{3} - \frac{4}{5} }= y^{\frac{-7}{15}}\\=\frac{1}{\sqrt[15]{ y^{7} }}=\frac{1}{\sqrt[15]{ y^{7} }}. \color{purple}{\frac{\sqrt[15]{ y^{8} }}{\sqrt[15]{ y^{8} }}} \\=\frac{\sqrt[15]{ y^{8} }}{y}\\---------------\)
4. \(\dfrac{q^{-1}}{q^{\frac{-1}{2}}}\\= q^{ -1 - (\frac{-1}{2}) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
5. \(\dfrac{q^{\frac{5}{4}}}{q^{-1}}\\= q^{ \frac{5}{4} - (-1) }= q^{\frac{9}{4}}\\=\sqrt[4]{ q^{9} }=|q^{2}|.\sqrt[4]{ q }\\---------------\)
6. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-1}{3} - \frac{1}{3} }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
7. \(\dfrac{y^{\frac{-3}{2}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{-3}{2} - (\frac{-4}{3}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
8. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{-1}{4}}}\\= y^{ \frac{-5}{2} - (\frac{-1}{4}) }= y^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ y^{9} }}\\=\frac{1}{|y^{2}|.\sqrt[4]{ y }}=\frac{1}{|y^{2}|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{3}|}\\---------------\)
9. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{1}{3}}}\\= q^{ \frac{-1}{2} - \frac{1}{3} }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
10. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-3}{2}}}\\= x^{ \frac{-1}{2} - (\frac{-3}{2}) }= x^{1}\\\\---------------\)
11. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-5}{4}}}\\= y^{ \frac{-1}{3} - (\frac{-5}{4}) }= y^{\frac{11}{12}}\\=\sqrt[12]{ y^{11} }\\---------------\)
12. \(\dfrac{y^{\frac{1}{3}}}{y^{1}}\\= y^{ \frac{1}{3} - 1 }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)