Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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