Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-4}{5}}}{q^{2}}\\= q^{ \frac{-4}{5} - 2 }= q^{\frac{-14}{5}}\\=\frac{1}{\sqrt[5]{ q^{14} }}\\=\frac{1}{q^{2}.\sqrt[5]{ q^{4} }}=\frac{1}{q^{2}.\sqrt[5]{ q^{4} }} \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q^{3}}\\---------------\)
2. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-1}{4}}}\\= q^{ \frac{1}{2} - (\frac{-1}{4}) }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
3. \(\dfrac{x^{\frac{-3}{2}}}{x^{2}}\\= x^{ \frac{-3}{2} - 2 }= x^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ x^{7} } }\\=\frac{1}{|x^{3}|. \sqrt{ x } }=\frac{1}{|x^{3}|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{4}|}\\---------------\)
4. \(\dfrac{q^{\frac{3}{4}}}{q^{-1}}\\= q^{ \frac{3}{4} - (-1) }= q^{\frac{7}{4}}\\=\sqrt[4]{ q^{7} }=|q|.\sqrt[4]{ q^{3} }\\---------------\)
5. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{-1}{5}}}\\= y^{ \frac{3}{4} - (\frac{-1}{5}) }= y^{\frac{19}{20}}\\=\sqrt[20]{ y^{19} }\\---------------\)
6. \(\dfrac{y^{1}}{y^{\frac{-1}{3}}}\\= y^{ 1 - (\frac{-1}{3}) }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
7. \(\dfrac{a^{\frac{-5}{4}}}{a^{-1}}\\= a^{ \frac{-5}{4} - (-1) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
8. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-5}{2}}}\\= a^{ \frac{2}{3} - (\frac{-5}{2}) }= a^{\frac{19}{6}}\\=\sqrt[6]{ a^{19} }=|a^{3}|.\sqrt[6]{ a }\\---------------\)
9. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{1}{3} - (\frac{-2}{3}) }= y^{1}\\\\---------------\)
10. \(\dfrac{x^{\frac{4}{5}}}{x^{-1}}\\= x^{ \frac{4}{5} - (-1) }= x^{\frac{9}{5}}\\=\sqrt[5]{ x^{9} }=x.\sqrt[5]{ x^{4} }\\---------------\)
11. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{4}{3}}}\\= a^{ \frac{5}{3} - \frac{4}{3} }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
12. \(\dfrac{q^{\frac{-5}{3}}}{q^{-1}}\\= q^{ \frac{-5}{3} - (-1) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)