Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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