Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{2}{3}}}\\= q^{ \frac{-1}{2} - \frac{2}{3} }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)
2. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-1}{4}}}\\= a^{ \frac{2}{3} - (\frac{-1}{4}) }= a^{\frac{11}{12}}\\=\sqrt[12]{ a^{11} }\\---------------\)
3. \(\dfrac{a^{1}}{a^{-1}}\\= a^{ 1 - (-1) }= a^{2}\\\\---------------\)
4. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{5}{6} - (\frac{-1}{3}) }= q^{\frac{7}{6}}\\=\sqrt[6]{ q^{7} }=|q|.\sqrt[6]{ q }\\---------------\)
5. \(\dfrac{q^{\frac{-2}{3}}}{q^{-1}}\\= q^{ \frac{-2}{3} - (-1) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
6. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-1}{3} - (\frac{-1}{3}) }= q^{0}\\=1\\---------------\)
7. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{4}{5}}}\\= x^{ \frac{-4}{5} - \frac{4}{5} }= x^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ x^{8} }}\\=\frac{1}{x.\sqrt[5]{ x^{3} }}=\frac{1}{x.\sqrt[5]{ x^{3} }} \color{purple}{\frac{\sqrt[5]{ x^{2} }}{\sqrt[5]{ x^{2} }}} \\=\frac{\sqrt[5]{ x^{2} }}{x^{2}}\\---------------\)
8. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-3}{4}}}\\= a^{ \frac{1}{2} - (\frac{-3}{4}) }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)
9. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{-4}{5}}}\\= x^{ \frac{1}{3} - (\frac{-4}{5}) }= x^{\frac{17}{15}}\\=\sqrt[15]{ x^{17} }=x.\sqrt[15]{ x^{2} }\\---------------\)
10. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{1}{4}}}\\= x^{ \frac{-1}{3} - \frac{1}{4} }= x^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ x^{7} }}=\frac{1}{\sqrt[12]{ x^{7} }}. \color{purple}{\frac{\sqrt[12]{ x^{5} }}{\sqrt[12]{ x^{5} }}} \\=\frac{\sqrt[12]{ x^{5} }}{|x|}\\---------------\)
11. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{1}{5}}}\\= x^{ \frac{-3}{5} - \frac{1}{5} }= x^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ x^{4} }}=\frac{1}{\sqrt[5]{ x^{4} }}. \color{purple}{\frac{\sqrt[5]{ x }}{\sqrt[5]{ x }}} \\=\frac{\sqrt[5]{ x }}{x}\\---------------\)
12. \(\dfrac{y^{1}}{y^{\frac{5}{4}}}\\= y^{ 1 - \frac{5}{4} }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)