Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-5}{3}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-5}{3} - (\frac{-1}{3}) }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
2. \(\dfrac{x^{-1}}{x^{\frac{1}{4}}}\\= x^{ -1 - \frac{1}{4} }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
3. \(\dfrac{a^{-1}}{a^{\frac{-5}{2}}}\\= a^{ -1 - (\frac{-5}{2}) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
4. \(\dfrac{y^{\frac{1}{6}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{1}{6} - (\frac{-5}{2}) }= y^{\frac{8}{3}}\\=\sqrt[3]{ y^{8} }=y^{2}.\sqrt[3]{ y^{2} }\\---------------\)
5. \(\dfrac{y^{\frac{-3}{2}}}{y^{\frac{4}{5}}}\\= y^{ \frac{-3}{2} - \frac{4}{5} }= y^{\frac{-23}{10}}\\=\frac{1}{\sqrt[10]{ y^{23} }}\\=\frac{1}{|y^{2}|.\sqrt[10]{ y^{3} }}=\frac{1}{|y^{2}|.\sqrt[10]{ y^{3} }} \color{purple}{\frac{\sqrt[10]{ y^{7} }}{\sqrt[10]{ y^{7} }}} \\=\frac{\sqrt[10]{ y^{7} }}{|y^{3}|}\\---------------\)
6. \(\dfrac{q^{\frac{-2}{5}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{-2}{5} - (\frac{-4}{5}) }= q^{\frac{2}{5}}\\=\sqrt[5]{ q^{2} }\\---------------\)
7. \(\dfrac{a^{\frac{-5}{4}}}{a^{\frac{5}{3}}}\\= a^{ \frac{-5}{4} - \frac{5}{3} }= a^{\frac{-35}{12}}\\=\frac{1}{\sqrt[12]{ a^{35} }}\\=\frac{1}{|a^{2}|.\sqrt[12]{ a^{11} }}=\frac{1}{|a^{2}|.\sqrt[12]{ a^{11} }} \color{purple}{\frac{\sqrt[12]{ a }}{\sqrt[12]{ a }}} \\=\frac{\sqrt[12]{ a }}{|a^{3}|}\\---------------\)
8. \(\dfrac{q^{2}}{q^{\frac{1}{2}}}\\= q^{ 2 - \frac{1}{2} }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
9. \(\dfrac{y^{1}}{y^{2}}\\= y^{ 1 - 2 }= y^{-1}\\=\frac{1}{y}\\---------------\)
10. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{3}{5} - (\frac{-3}{5}) }= y^{\frac{6}{5}}\\=\sqrt[5]{ y^{6} }=y.\sqrt[5]{ y }\\---------------\)
11. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-4}{5} - (\frac{-1}{2}) }= y^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ y^{3} }}=\frac{1}{\sqrt[10]{ y^{3} }}. \color{purple}{\frac{\sqrt[10]{ y^{7} }}{\sqrt[10]{ y^{7} }}} \\=\frac{\sqrt[10]{ y^{7} }}{|y|}\\---------------\)
12. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-1}{3} - (\frac{-1}{2}) }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)