Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-4}{3}}}{a^{\frac{-4}{3}}}\\= a^{ \frac{-4}{3} - (\frac{-4}{3}) }= a^{0}\\=1\\---------------\)
2. \(\dfrac{a^{2}}{a^{2}}\\= a^{ 2 - 2 }= a^{0}\\=1\\---------------\)
3. \(\dfrac{y^{\frac{-2}{5}}}{y^{\frac{3}{2}}}\\= y^{ \frac{-2}{5} - \frac{3}{2} }= y^{\frac{-19}{10}}\\=\frac{1}{\sqrt[10]{ y^{19} }}\\=\frac{1}{|y|.\sqrt[10]{ y^{9} }}=\frac{1}{|y|.\sqrt[10]{ y^{9} }} \color{purple}{\frac{\sqrt[10]{ y }}{\sqrt[10]{ y }}} \\=\frac{\sqrt[10]{ y }}{|y^{2}|}\\---------------\)
4. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{-4}{5}}}\\= y^{ \frac{1}{3} - (\frac{-4}{5}) }= y^{\frac{17}{15}}\\=\sqrt[15]{ y^{17} }=y.\sqrt[15]{ y^{2} }\\---------------\)
5. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{-2}{5}}}\\= x^{ \frac{-5}{3} - (\frac{-2}{5}) }= x^{\frac{-19}{15}}\\=\frac{1}{\sqrt[15]{ x^{19} }}\\=\frac{1}{x.\sqrt[15]{ x^{4} }}=\frac{1}{x.\sqrt[15]{ x^{4} }} \color{purple}{\frac{\sqrt[15]{ x^{11} }}{\sqrt[15]{ x^{11} }}} \\=\frac{\sqrt[15]{ x^{11} }}{x^{2}}\\---------------\)
6. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{3}{5}}}\\= q^{ \frac{5}{6} - \frac{3}{5} }= q^{\frac{7}{30}}\\=\sqrt[30]{ q^{7} }\\---------------\)
7. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{3}{4}}}\\= y^{ \frac{-2}{3} - \frac{3}{4} }= y^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ y^{17} }}\\=\frac{1}{|y|.\sqrt[12]{ y^{5} }}=\frac{1}{|y|.\sqrt[12]{ y^{5} }} \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y^{2}|}\\---------------\)
8. \(\dfrac{y^{\frac{-3}{2}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-3}{2} - \frac{1}{2} }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
9. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{5}{6}}}\\= x^{ \frac{5}{3} - \frac{5}{6} }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
10. \(\dfrac{x^{\frac{-1}{5}}}{x^{1}}\\= x^{ \frac{-1}{5} - 1 }= x^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ x^{6} }}\\=\frac{1}{x.\sqrt[5]{ x }}=\frac{1}{x.\sqrt[5]{ x }} \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x^{2}}\\---------------\)
11. \(\dfrac{x^{1}}{x^{1}}\\= x^{ 1 - 1 }= x^{0}\\=1\\---------------\)
12. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{2}{3}}}\\= q^{ \frac{-2}{3} - \frac{2}{3} }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)