Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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