Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-3}{2}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-3}{2} - \frac{1}{2} }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
2. \(\dfrac{x^{\frac{1}{6}}}{x^{-1}}\\= x^{ \frac{1}{6} - (-1) }= x^{\frac{7}{6}}\\=\sqrt[6]{ x^{7} }=|x|.\sqrt[6]{ x }\\---------------\)
3. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{-3}{5}}}\\= q^{ \frac{1}{4} - (\frac{-3}{5}) }= q^{\frac{17}{20}}\\=\sqrt[20]{ q^{17} }\\---------------\)
4. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{1}{2} - (\frac{-1}{2}) }= x^{1}\\\\---------------\)
5. \(\dfrac{a^{\frac{-5}{2}}}{a^{\frac{-3}{4}}}\\= a^{ \frac{-5}{2} - (\frac{-3}{4}) }= a^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[4]{ a^{3} }}=\frac{1}{|a|.\sqrt[4]{ a^{3} }} \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a^{2}|}\\---------------\)
6. \(\dfrac{y^{\frac{5}{4}}}{y^{1}}\\= y^{ \frac{5}{4} - 1 }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
7. \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{-5}{2} - (\frac{-1}{3}) }= x^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ x^{13} }}\\=\frac{1}{|x^{2}|.\sqrt[6]{ x }}=\frac{1}{|x^{2}|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{3}|}\\---------------\)
8. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-1}{2} - (\frac{-1}{3}) }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
9. \(\dfrac{y^{\frac{1}{5}}}{y^{\frac{-5}{6}}}\\= y^{ \frac{1}{5} - (\frac{-5}{6}) }= y^{\frac{31}{30}}\\=\sqrt[30]{ y^{31} }=|y|.\sqrt[30]{ y }\\---------------\)
10. \(\dfrac{x^{-1}}{x^{-1}}\\= x^{ -1 - (-1) }= x^{0}\\=1\\---------------\)
11. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{1}{6}}}\\= y^{ \frac{-2}{3} - \frac{1}{6} }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
12. \(\dfrac{y^{\frac{1}{5}}}{y^{\frac{-5}{4}}}\\= y^{ \frac{1}{5} - (\frac{-5}{4}) }= y^{\frac{29}{20}}\\=\sqrt[20]{ y^{29} }=|y|.\sqrt[20]{ y^{9} }\\---------------\)