Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-4}{3}}}{q^{-1}}\\= q^{ \frac{-4}{3} - (-1) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
2. \(\dfrac{a^{\frac{3}{4}}}{a^{\frac{-3}{2}}}\\= a^{ \frac{3}{4} - (\frac{-3}{2}) }= a^{\frac{9}{4}}\\=\sqrt[4]{ a^{9} }=|a^{2}|.\sqrt[4]{ a }\\---------------\)
3. \(\dfrac{a^{\frac{-4}{5}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-4}{5} - (\frac{-1}{3}) }= a^{\frac{-7}{15}}\\=\frac{1}{\sqrt[15]{ a^{7} }}=\frac{1}{\sqrt[15]{ a^{7} }}. \color{purple}{\frac{\sqrt[15]{ a^{8} }}{\sqrt[15]{ a^{8} }}} \\=\frac{\sqrt[15]{ a^{8} }}{a}\\---------------\)
4. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-5}{4} - \frac{1}{2} }= y^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[4]{ y^{3} }}=\frac{1}{|y|.\sqrt[4]{ y^{3} }} \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y^{2}|}\\---------------\)
5. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{5}{4} - (\frac{-4}{3}) }= x^{\frac{31}{12}}\\=\sqrt[12]{ x^{31} }=|x^{2}|.\sqrt[12]{ x^{7} }\\---------------\)
6. \(\dfrac{q^{\frac{5}{2}}}{q^{2}}\\= q^{ \frac{5}{2} - 2 }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
7. \(\dfrac{q^{-1}}{q^{-1}}\\= q^{ -1 - (-1) }= q^{0}\\=1\\---------------\)
8. \(\dfrac{x^{\frac{-4}{5}}}{x^{1}}\\= x^{ \frac{-4}{5} - 1 }= x^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ x^{9} }}\\=\frac{1}{x.\sqrt[5]{ x^{4} }}=\frac{1}{x.\sqrt[5]{ x^{4} }} \color{purple}{\frac{\sqrt[5]{ x }}{\sqrt[5]{ x }}} \\=\frac{\sqrt[5]{ x }}{x^{2}}\\---------------\)
9. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{1}{3}}}\\= a^{ \frac{1}{4} - \frac{1}{3} }= a^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ a }}=\frac{1}{\sqrt[12]{ a }}. \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a|}\\---------------\)
10. \(\dfrac{q^{-1}}{q^{\frac{-2}{5}}}\\= q^{ -1 - (\frac{-2}{5}) }= q^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ q^{3} }}=\frac{1}{\sqrt[5]{ q^{3} }}. \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q}\\---------------\)
11. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{-1}{2} - (\frac{-1}{3}) }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
12. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{1}{6}}}\\= x^{ \frac{1}{2} - \frac{1}{6} }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)