Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-1}{2}}}{x^{1}}\\= x^{ \frac{-1}{2} - 1 }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
2. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-3}{4}}}\\= q^{ \frac{-1}{2} - (\frac{-3}{4}) }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
3. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{1}{3} - (\frac{-1}{3}) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
4. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-5}{2}}}\\= a^{ \frac{-1}{3} - (\frac{-5}{2}) }= a^{\frac{13}{6}}\\=\sqrt[6]{ a^{13} }=|a^{2}|.\sqrt[6]{ a }\\---------------\)
5. \(\dfrac{q^{\frac{-1}{5}}}{q^{1}}\\= q^{ \frac{-1}{5} - 1 }= q^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ q^{6} }}\\=\frac{1}{q.\sqrt[5]{ q }}=\frac{1}{q.\sqrt[5]{ q }} \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q^{2}}\\---------------\)
6. \(\dfrac{a^{\frac{-4}{3}}}{a^{\frac{5}{6}}}\\= a^{ \frac{-4}{3} - \frac{5}{6} }= a^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ a^{13} }}\\=\frac{1}{|a^{2}|.\sqrt[6]{ a }}=\frac{1}{|a^{2}|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{3}|}\\---------------\)
7. \(\dfrac{q^{1}}{q^{\frac{-1}{2}}}\\= q^{ 1 - (\frac{-1}{2}) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
8. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{1}{3}}}\\= a^{ \frac{1}{3} - \frac{1}{3} }= a^{0}\\=1\\---------------\)
9. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{-1}{2} - (\frac{-5}{2}) }= y^{2}\\\\---------------\)
10. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-5}{6}}}\\= y^{ \frac{-1}{3} - (\frac{-5}{6}) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
11. \(\dfrac{y^{1}}{y^{1}}\\= y^{ 1 - 1 }= y^{0}\\=1\\---------------\)
12. \(\dfrac{y^{-1}}{y^{\frac{-3}{5}}}\\= y^{ -1 - (\frac{-3}{5}) }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)