Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{-1}}{a^{\frac{-5}{2}}}\\= a^{ -1 - (\frac{-5}{2}) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
2. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{1}{2} - (\frac{-1}{2}) }= y^{1}\\\\---------------\)
3. \(\dfrac{y^{\frac{-3}{2}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-3}{2} - (\frac{-1}{2}) }= y^{-1}\\=\frac{1}{y}\\---------------\)
4. \(\dfrac{x^{-1}}{x^{\frac{-1}{6}}}\\= x^{ -1 - (\frac{-1}{6}) }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
5. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{-5}{6} - (\frac{-2}{3}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
6. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{1}{2} - (\frac{-1}{3}) }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
7. \(\dfrac{x^{\frac{-5}{6}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-5}{6} - (\frac{-1}{2}) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
8. \(\dfrac{a^{\frac{1}{5}}}{a^{\frac{-4}{3}}}\\= a^{ \frac{1}{5} - (\frac{-4}{3}) }= a^{\frac{23}{15}}\\=\sqrt[15]{ a^{23} }=a.\sqrt[15]{ a^{8} }\\---------------\)
9. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{4}{5}}}\\= x^{ \frac{2}{3} - \frac{4}{5} }= x^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ x^{2} }}=\frac{1}{\sqrt[15]{ x^{2} }}. \color{purple}{\frac{\sqrt[15]{ x^{13} }}{\sqrt[15]{ x^{13} }}} \\=\frac{\sqrt[15]{ x^{13} }}{x}\\---------------\)
10. \(\dfrac{y^{\frac{5}{6}}}{y^{\frac{5}{2}}}\\= y^{ \frac{5}{6} - \frac{5}{2} }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
11. \(\dfrac{q^{\frac{-3}{4}}}{q^{-2}}\\= q^{ \frac{-3}{4} - (-2) }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
12. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{2}{3} - (\frac{-3}{4}) }= x^{\frac{17}{12}}\\=\sqrt[12]{ x^{17} }=|x|.\sqrt[12]{ x^{5} }\\---------------\)