Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{3}{4}}}\\= a^{ \frac{1}{2} - \frac{3}{4} }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
2. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{-4}{5}}}\\= x^{ \frac{4}{5} - (\frac{-4}{5}) }= x^{\frac{8}{5}}\\=\sqrt[5]{ x^{8} }=x.\sqrt[5]{ x^{3} }\\---------------\)
3. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{-3}{5} - (\frac{-2}{3}) }= q^{\frac{1}{15}}\\=\sqrt[15]{ q }\\---------------\)
4. \(\dfrac{a^{\frac{3}{2}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{3}{2} - (\frac{-1}{6}) }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
5. \(\dfrac{x^{\frac{5}{6}}}{x^{-1}}\\= x^{ \frac{5}{6} - (-1) }= x^{\frac{11}{6}}\\=\sqrt[6]{ x^{11} }=|x|.\sqrt[6]{ x^{5} }\\---------------\)
6. \(\dfrac{a^{\frac{3}{5}}}{a^{-2}}\\= a^{ \frac{3}{5} - (-2) }= a^{\frac{13}{5}}\\=\sqrt[5]{ a^{13} }=a^{2}.\sqrt[5]{ a^{3} }\\---------------\)
7. \(\dfrac{a^{\frac{3}{2}}}{a^{1}}\\= a^{ \frac{3}{2} - 1 }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
8. \(\dfrac{q^{\frac{5}{4}}}{q^{\frac{1}{3}}}\\= q^{ \frac{5}{4} - \frac{1}{3} }= q^{\frac{11}{12}}\\=\sqrt[12]{ q^{11} }\\---------------\)
9. \(\dfrac{y^{\frac{-5}{3}}}{y^{\frac{4}{3}}}\\= y^{ \frac{-5}{3} - \frac{4}{3} }= y^{-3}\\=\frac{1}{y^{3}}\\---------------\)
10. \(\dfrac{x^{\frac{-3}{2}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-3}{2} - \frac{1}{3} }= x^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ x^{11} }}\\=\frac{1}{|x|.\sqrt[6]{ x^{5} }}=\frac{1}{|x|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{2}|}\\---------------\)
11. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-1}{2} - (\frac{-1}{3}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
12. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-2}{3} - (\frac{-1}{3}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)