Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{-1}}{a^{\frac{-3}{5}}}\\= a^{ -1 - (\frac{-3}{5}) }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
2. \(\dfrac{a^{1}}{a^{1}}\\= a^{ 1 - 1 }= a^{0}\\=1\\---------------\)
3. \(\dfrac{a^{1}}{a^{\frac{-1}{2}}}\\= a^{ 1 - (\frac{-1}{2}) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
4. \(\dfrac{a^{\frac{1}{3}}}{a^{1}}\\= a^{ \frac{1}{3} - 1 }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
5. \(\dfrac{x^{1}}{x^{\frac{-3}{5}}}\\= x^{ 1 - (\frac{-3}{5}) }= x^{\frac{8}{5}}\\=\sqrt[5]{ x^{8} }=x.\sqrt[5]{ x^{3} }\\---------------\)
6. \(\dfrac{a^{\frac{-3}{5}}}{a^{\frac{3}{4}}}\\= a^{ \frac{-3}{5} - \frac{3}{4} }= a^{\frac{-27}{20}}\\=\frac{1}{\sqrt[20]{ a^{27} }}\\=\frac{1}{|a|.\sqrt[20]{ a^{7} }}=\frac{1}{|a|.\sqrt[20]{ a^{7} }} \color{purple}{\frac{\sqrt[20]{ a^{13} }}{\sqrt[20]{ a^{13} }}} \\=\frac{\sqrt[20]{ a^{13} }}{|a^{2}|}\\---------------\)
7. \(\dfrac{q^{-1}}{q^{\frac{2}{5}}}\\= q^{ -1 - \frac{2}{5} }= q^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ q^{7} }}\\=\frac{1}{q.\sqrt[5]{ q^{2} }}=\frac{1}{q.\sqrt[5]{ q^{2} }} \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q^{2}}\\---------------\)
8. \(\dfrac{y^{\frac{1}{6}}}{y^{-1}}\\= y^{ \frac{1}{6} - (-1) }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)
9. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{3}{4} - (\frac{-5}{4}) }= x^{2}\\\\---------------\)
10. \(\dfrac{q^{\frac{1}{5}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{1}{5} - (\frac{-1}{2}) }= q^{\frac{7}{10}}\\=\sqrt[10]{ q^{7} }\\---------------\)
11. \(\dfrac{x^{-1}}{x^{\frac{5}{3}}}\\= x^{ -1 - \frac{5}{3} }= x^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ x^{8} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x^{2} }}=\frac{1}{x^{2}.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{3}}\\---------------\)
12. \(\dfrac{x^{\frac{-3}{4}}}{x^{\frac{-3}{2}}}\\= x^{ \frac{-3}{4} - (\frac{-3}{2}) }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)