Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-4}{5}}}{q^{\frac{5}{2}}}\\= q^{ \frac{-4}{5} - \frac{5}{2} }= q^{\frac{-33}{10}}\\=\frac{1}{\sqrt[10]{ q^{33} }}\\=\frac{1}{|q^{3}|.\sqrt[10]{ q^{3} }}=\frac{1}{|q^{3}|.\sqrt[10]{ q^{3} }} \color{purple}{\frac{\sqrt[10]{ q^{7} }}{\sqrt[10]{ q^{7} }}} \\=\frac{\sqrt[10]{ q^{7} }}{|q^{4}|}\\---------------\)
2. \(\dfrac{q^{-1}}{q^{\frac{2}{3}}}\\= q^{ -1 - \frac{2}{3} }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
3. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{-1}{3} - (\frac{-5}{3}) }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
4. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{2}{3}}}\\= x^{ \frac{3}{2} - \frac{2}{3} }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
5. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{1}{4} - (\frac{-1}{2}) }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
6. \(\dfrac{x^{1}}{x^{\frac{2}{3}}}\\= x^{ 1 - \frac{2}{3} }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
7. \(\dfrac{y^{\frac{5}{4}}}{y^{\frac{2}{5}}}\\= y^{ \frac{5}{4} - \frac{2}{5} }= y^{\frac{17}{20}}\\=\sqrt[20]{ y^{17} }\\---------------\)
8. \(\dfrac{y^{1}}{y^{\frac{3}{4}}}\\= y^{ 1 - \frac{3}{4} }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
9. \(\dfrac{q^{\frac{1}{5}}}{q^{\frac{5}{3}}}\\= q^{ \frac{1}{5} - \frac{5}{3} }= q^{\frac{-22}{15}}\\=\frac{1}{\sqrt[15]{ q^{22} }}\\=\frac{1}{q.\sqrt[15]{ q^{7} }}=\frac{1}{q.\sqrt[15]{ q^{7} }} \color{purple}{\frac{\sqrt[15]{ q^{8} }}{\sqrt[15]{ q^{8} }}} \\=\frac{\sqrt[15]{ q^{8} }}{q^{2}}\\---------------\)
10. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-5}{6}}}\\= x^{ \frac{-1}{2} - (\frac{-5}{6}) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
11. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{2}{5} - (\frac{-2}{3}) }= a^{\frac{16}{15}}\\=\sqrt[15]{ a^{16} }=a.\sqrt[15]{ a }\\---------------\)
12. \(\dfrac{a^{\frac{4}{3}}}{a^{-1}}\\= a^{ \frac{4}{3} - (-1) }= a^{\frac{7}{3}}\\=\sqrt[3]{ a^{7} }=a^{2}.\sqrt[3]{ a }\\---------------\)