Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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