Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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