Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-1}{4}}}{q^{1}}\\= q^{ \frac{-1}{4} - 1 }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
2. \(\dfrac{y^{\frac{-3}{2}}}{y^{\frac{-3}{2}}}\\= y^{ \frac{-3}{2} - (\frac{-3}{2}) }= y^{0}\\=1\\---------------\)
3. \(\dfrac{q^{\frac{-4}{5}}}{q^{1}}\\= q^{ \frac{-4}{5} - 1 }= q^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ q^{9} }}\\=\frac{1}{q.\sqrt[5]{ q^{4} }}=\frac{1}{q.\sqrt[5]{ q^{4} }} \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q^{2}}\\---------------\)
4. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{3}{5} - (\frac{-1}{2}) }= a^{\frac{11}{10}}\\=\sqrt[10]{ a^{11} }=|a|.\sqrt[10]{ a }\\---------------\)
5. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{3}{2} - (\frac{-3}{4}) }= x^{\frac{9}{4}}\\=\sqrt[4]{ x^{9} }=|x^{2}|.\sqrt[4]{ x }\\---------------\)
6. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{-1}{4}}}\\= y^{ \frac{3}{4} - (\frac{-1}{4}) }= y^{1}\\\\---------------\)
7. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{5}{2} - (\frac{-1}{2}) }= y^{3}\\\\---------------\)
8. \(\dfrac{q^{\frac{5}{2}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{5}{2} - (\frac{-2}{5}) }= q^{\frac{29}{10}}\\=\sqrt[10]{ q^{29} }=|q^{2}|.\sqrt[10]{ q^{9} }\\---------------\)
9. \(\dfrac{a^{\frac{1}{3}}}{a^{1}}\\= a^{ \frac{1}{3} - 1 }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
10. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{5}{6}}}\\= a^{ \frac{-1}{3} - \frac{5}{6} }= a^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[6]{ a }}=\frac{1}{|a|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{2}|}\\---------------\)
11. \(\dfrac{a^{\frac{-1}{6}}}{a^{\frac{1}{4}}}\\= a^{ \frac{-1}{6} - \frac{1}{4} }= a^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ a^{5} }}=\frac{1}{\sqrt[12]{ a^{5} }}. \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a|}\\---------------\)
12. \(\dfrac{q^{-1}}{q^{\frac{-4}{5}}}\\= q^{ -1 - (\frac{-4}{5}) }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)