Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{1}}{a^{\frac{-1}{2}}}\\= a^{ 1 - (\frac{-1}{2}) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
2. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{2}{5}}}\\= a^{ \frac{4}{5} - \frac{2}{5} }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
3. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{2}{3}}}\\= x^{ \frac{3}{4} - \frac{2}{3} }= x^{\frac{1}{12}}\\=\sqrt[12]{ x }\\---------------\)
4. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{-1}{3} - (\frac{-4}{3}) }= q^{1}\\\\---------------\)
5. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{-3}{5}}}\\= q^{ \frac{-5}{2} - (\frac{-3}{5}) }= q^{\frac{-19}{10}}\\=\frac{1}{\sqrt[10]{ q^{19} }}\\=\frac{1}{|q|.\sqrt[10]{ q^{9} }}=\frac{1}{|q|.\sqrt[10]{ q^{9} }} \color{purple}{\frac{\sqrt[10]{ q }}{\sqrt[10]{ q }}} \\=\frac{\sqrt[10]{ q }}{|q^{2}|}\\---------------\)
6. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{5}{6}}}\\= q^{ \frac{5}{6} - \frac{5}{6} }= q^{0}\\=1\\---------------\)
7. \(\dfrac{y^{1}}{y^{\frac{4}{3}}}\\= y^{ 1 - \frac{4}{3} }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
8. \(\dfrac{x^{-1}}{x^{-1}}\\= x^{ -1 - (-1) }= x^{0}\\=1\\---------------\)
9. \(\dfrac{a^{\frac{-2}{5}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{-2}{5} - (\frac{-2}{3}) }= a^{\frac{4}{15}}\\=\sqrt[15]{ a^{4} }\\---------------\)
10. \(\dfrac{y^{\frac{-1}{4}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-1}{4} - \frac{1}{2} }= y^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ y^{3} }}=\frac{1}{\sqrt[4]{ y^{3} }}. \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y|}\\---------------\)
11. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{2}{3}}}\\= a^{ \frac{1}{2} - \frac{2}{3} }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
12. \(\dfrac{q^{\frac{3}{5}}}{q^{\frac{-3}{2}}}\\= q^{ \frac{3}{5} - (\frac{-3}{2}) }= q^{\frac{21}{10}}\\=\sqrt[10]{ q^{21} }=|q^{2}|.\sqrt[10]{ q }\\---------------\)