Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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