Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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