Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{1}}{a^{-1}}\\= a^{ 1 - (-1) }= a^{2}\\\\---------------\)
2. \(\dfrac{q^{-1}}{q^{1}}\\= q^{ -1 - 1 }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
3. \(\dfrac{a^{\frac{-3}{2}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{-3}{2} - (\frac{-1}{6}) }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
4. \(\dfrac{a^{\frac{1}{3}}}{a^{-2}}\\= a^{ \frac{1}{3} - (-2) }= a^{\frac{7}{3}}\\=\sqrt[3]{ a^{7} }=a^{2}.\sqrt[3]{ a }\\---------------\)
5. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-1}{2} - (\frac{-1}{2}) }= y^{0}\\=1\\---------------\)
6. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-5}{2} - \frac{1}{3} }= y^{\frac{-17}{6}}\\=\frac{1}{\sqrt[6]{ y^{17} }}\\=\frac{1}{|y^{2}|.\sqrt[6]{ y^{5} }}=\frac{1}{|y^{2}|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{3}|}\\---------------\)
7. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{4}{3}}}\\= x^{ \frac{4}{5} - \frac{4}{3} }= x^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ x^{8} }}=\frac{1}{\sqrt[15]{ x^{8} }}. \color{purple}{\frac{\sqrt[15]{ x^{7} }}{\sqrt[15]{ x^{7} }}} \\=\frac{\sqrt[15]{ x^{7} }}{x}\\---------------\)
8. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{-3}{4} - (\frac{-4}{5}) }= q^{\frac{1}{20}}\\=\sqrt[20]{ q }\\---------------\)
9. \(\dfrac{x^{\frac{3}{2}}}{x^{-1}}\\= x^{ \frac{3}{2} - (-1) }= x^{\frac{5}{2}}\\= \sqrt{ x^{5} } =|x^{2}|. \sqrt{ x } \\---------------\)
10. \(\dfrac{y^{-1}}{y^{-1}}\\= y^{ -1 - (-1) }= y^{0}\\=1\\---------------\)
11. \(\dfrac{x^{-1}}{x^{\frac{-4}{3}}}\\= x^{ -1 - (\frac{-4}{3}) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
12. \(\dfrac{y^{\frac{-1}{4}}}{y^{\frac{3}{5}}}\\= y^{ \frac{-1}{4} - \frac{3}{5} }= y^{\frac{-17}{20}}\\=\frac{1}{\sqrt[20]{ y^{17} }}=\frac{1}{\sqrt[20]{ y^{17} }}. \color{purple}{\frac{\sqrt[20]{ y^{3} }}{\sqrt[20]{ y^{3} }}} \\=\frac{\sqrt[20]{ y^{3} }}{|y|}\\---------------\)