Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{-1}}{x^{1}}\\= x^{ -1 - 1 }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
2. \(\dfrac{a^{1}}{a^{\frac{-1}{3}}}\\= a^{ 1 - (\frac{-1}{3}) }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
3. \(\dfrac{q^{\frac{-3}{2}}}{q^{1}}\\= q^{ \frac{-3}{2} - 1 }= q^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ q^{5} } }\\=\frac{1}{|q^{2}|. \sqrt{ q } }=\frac{1}{|q^{2}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{3}|}\\---------------\)
4. \(\dfrac{y^{-1}}{y^{\frac{3}{5}}}\\= y^{ -1 - \frac{3}{5} }= y^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ y^{8} }}\\=\frac{1}{y.\sqrt[5]{ y^{3} }}=\frac{1}{y.\sqrt[5]{ y^{3} }} \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y^{2}}\\---------------\)
5. \(\dfrac{x^{1}}{x^{1}}\\= x^{ 1 - 1 }= x^{0}\\=1\\---------------\)
6. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{2}{3}}}\\= q^{ \frac{-1}{3} - \frac{2}{3} }= q^{-1}\\=\frac{1}{q}\\---------------\)
7. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{-3}{4}}}\\= a^{ \frac{-5}{6} - (\frac{-3}{4}) }= a^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ a }}=\frac{1}{\sqrt[12]{ a }}. \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a|}\\---------------\)
8. \(\dfrac{a^{\frac{-1}{6}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{-1}{6} - (\frac{-2}{3}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
9. \(\dfrac{a^{\frac{4}{3}}}{a^{1}}\\= a^{ \frac{4}{3} - 1 }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
10. \(\dfrac{y^{\frac{1}{5}}}{y^{1}}\\= y^{ \frac{1}{5} - 1 }= y^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ y^{4} }}=\frac{1}{\sqrt[5]{ y^{4} }}. \color{purple}{\frac{\sqrt[5]{ y }}{\sqrt[5]{ y }}} \\=\frac{\sqrt[5]{ y }}{y}\\---------------\)
11. \(\dfrac{a^{\frac{-5}{4}}}{a^{\frac{5}{2}}}\\= a^{ \frac{-5}{4} - \frac{5}{2} }= a^{\frac{-15}{4}}\\=\frac{1}{\sqrt[4]{ a^{15} }}\\=\frac{1}{|a^{3}|.\sqrt[4]{ a^{3} }}=\frac{1}{|a^{3}|.\sqrt[4]{ a^{3} }} \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a^{4}|}\\---------------\)
12. \(\dfrac{x^{-1}}{x^{\frac{-3}{5}}}\\= x^{ -1 - (\frac{-3}{5}) }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)