Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{5}{2}}}{q^{\frac{4}{3}}}\\= q^{ \frac{5}{2} - \frac{4}{3} }= q^{\frac{7}{6}}\\=\sqrt[6]{ q^{7} }=|q|.\sqrt[6]{ q }\\---------------\)
2. \(\dfrac{a^{\frac{5}{3}}}{a^{-1}}\\= a^{ \frac{5}{3} - (-1) }= a^{\frac{8}{3}}\\=\sqrt[3]{ a^{8} }=a^{2}.\sqrt[3]{ a^{2} }\\---------------\)
3. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{4}{5}}}\\= a^{ \frac{2}{3} - \frac{4}{5} }= a^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ a^{2} }}=\frac{1}{\sqrt[15]{ a^{2} }}. \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a}\\---------------\)
4. \(\dfrac{y^{\frac{4}{3}}}{y^{1}}\\= y^{ \frac{4}{3} - 1 }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
5. \(\dfrac{q^{-1}}{q^{\frac{4}{3}}}\\= q^{ -1 - \frac{4}{3} }= q^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ q^{7} }}\\=\frac{1}{q^{2}.\sqrt[3]{ q }}=\frac{1}{q^{2}.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{3}}\\---------------\)
6. \(\dfrac{q^{-1}}{q^{\frac{3}{4}}}\\= q^{ -1 - \frac{3}{4} }= q^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[4]{ q^{3} }}=\frac{1}{|q|.\sqrt[4]{ q^{3} }} \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q^{2}|}\\---------------\)
7. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{4}{3}}}\\= q^{ \frac{-3}{2} - \frac{4}{3} }= q^{\frac{-17}{6}}\\=\frac{1}{\sqrt[6]{ q^{17} }}\\=\frac{1}{|q^{2}|.\sqrt[6]{ q^{5} }}=\frac{1}{|q^{2}|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{3}|}\\---------------\)
8. \(\dfrac{q^{\frac{-3}{4}}}{q^{1}}\\= q^{ \frac{-3}{4} - 1 }= q^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[4]{ q^{3} }}=\frac{1}{|q|.\sqrt[4]{ q^{3} }} \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q^{2}|}\\---------------\)
9. \(\dfrac{q^{\frac{3}{5}}}{q^{-1}}\\= q^{ \frac{3}{5} - (-1) }= q^{\frac{8}{5}}\\=\sqrt[5]{ q^{8} }=q.\sqrt[5]{ q^{3} }\\---------------\)
10. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{-1}{2} - (\frac{-2}{3}) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
11. \(\dfrac{q^{\frac{-4}{3}}}{q^{\frac{2}{5}}}\\= q^{ \frac{-4}{3} - \frac{2}{5} }= q^{\frac{-26}{15}}\\=\frac{1}{\sqrt[15]{ q^{26} }}\\=\frac{1}{q.\sqrt[15]{ q^{11} }}=\frac{1}{q.\sqrt[15]{ q^{11} }} \color{purple}{\frac{\sqrt[15]{ q^{4} }}{\sqrt[15]{ q^{4} }}} \\=\frac{\sqrt[15]{ q^{4} }}{q^{2}}\\---------------\)
12. \(\dfrac{q^{1}}{q^{1}}\\= q^{ 1 - 1 }= q^{0}\\=1\\---------------\)