Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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