Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{4}{3}}}{q^{-1}}\\= q^{ \frac{4}{3} - (-1) }= q^{\frac{7}{3}}\\=\sqrt[3]{ q^{7} }=q^{2}.\sqrt[3]{ q }\\---------------\)
2. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{-5}{3}}}\\= y^{ \frac{5}{2} - (\frac{-5}{3}) }= y^{\frac{25}{6}}\\=\sqrt[6]{ y^{25} }=|y^{4}|.\sqrt[6]{ y }\\---------------\)
3. \(\dfrac{a^{-2}}{a^{\frac{-5}{6}}}\\= a^{ -2 - (\frac{-5}{6}) }= a^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[6]{ a }}=\frac{1}{|a|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{2}|}\\---------------\)
4. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-4}{3}}}\\= a^{ \frac{-2}{3} - (\frac{-4}{3}) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
5. \(\dfrac{q^{1}}{q^{\frac{-5}{4}}}\\= q^{ 1 - (\frac{-5}{4}) }= q^{\frac{9}{4}}\\=\sqrt[4]{ q^{9} }=|q^{2}|.\sqrt[4]{ q }\\---------------\)
6. \(\dfrac{x^{\frac{-1}{3}}}{x^{2}}\\= x^{ \frac{-1}{3} - 2 }= x^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ x^{7} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x }}=\frac{1}{x^{2}.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{3}}\\---------------\)
7. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{2}{3} - (\frac{-4}{3}) }= q^{2}\\\\---------------\)
8. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{1}{5}}}\\= q^{ \frac{5}{3} - \frac{1}{5} }= q^{\frac{22}{15}}\\=\sqrt[15]{ q^{22} }=q.\sqrt[15]{ q^{7} }\\---------------\)
9. \(\dfrac{y^{\frac{-3}{5}}}{y^{1}}\\= y^{ \frac{-3}{5} - 1 }= y^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ y^{8} }}\\=\frac{1}{y.\sqrt[5]{ y^{3} }}=\frac{1}{y.\sqrt[5]{ y^{3} }} \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y^{2}}\\---------------\)
10. \(\dfrac{x^{\frac{-3}{2}}}{x^{\frac{3}{2}}}\\= x^{ \frac{-3}{2} - \frac{3}{2} }= x^{-3}\\=\frac{1}{x^{3}}\\---------------\)
11. \(\dfrac{q^{-1}}{q^{-1}}\\= q^{ -1 - (-1) }= q^{0}\\=1\\---------------\)
12. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{5}{6}}}\\= x^{ \frac{-4}{3} - \frac{5}{6} }= x^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ x^{13} }}\\=\frac{1}{|x^{2}|.\sqrt[6]{ x }}=\frac{1}{|x^{2}|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{3}|}\\---------------\)