Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{-2}}{y^{\frac{1}{4}}}\\= y^{ -2 - \frac{1}{4} }= y^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ y^{9} }}\\=\frac{1}{|y^{2}|.\sqrt[4]{ y }}=\frac{1}{|y^{2}|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{3}|}\\---------------\)
2. \(\dfrac{x^{\frac{-2}{3}}}{x^{-1}}\\= x^{ \frac{-2}{3} - (-1) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
3. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{1}{3} - (\frac{-1}{2}) }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
4. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-5}{3}}}\\= x^{ \frac{-1}{3} - (\frac{-5}{3}) }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)
5. \(\dfrac{q^{-2}}{q^{\frac{-4}{5}}}\\= q^{ -2 - (\frac{-4}{5}) }= q^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ q^{6} }}\\=\frac{1}{q.\sqrt[5]{ q }}=\frac{1}{q.\sqrt[5]{ q }} \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q^{2}}\\---------------\)
6. \(\dfrac{a^{-1}}{a^{\frac{1}{2}}}\\= a^{ -1 - \frac{1}{2} }= a^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ a^{3} } }\\=\frac{1}{|a|. \sqrt{ a } }=\frac{1}{|a|. \sqrt{ a } } \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a^{2}|}\\---------------\)
7. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{3}{2}}}\\= x^{ \frac{-4}{5} - \frac{3}{2} }= x^{\frac{-23}{10}}\\=\frac{1}{\sqrt[10]{ x^{23} }}\\=\frac{1}{|x^{2}|.\sqrt[10]{ x^{3} }}=\frac{1}{|x^{2}|.\sqrt[10]{ x^{3} }} \color{purple}{\frac{\sqrt[10]{ x^{7} }}{\sqrt[10]{ x^{7} }}} \\=\frac{\sqrt[10]{ x^{7} }}{|x^{3}|}\\---------------\)
8. \(\dfrac{q^{1}}{q^{\frac{1}{4}}}\\= q^{ 1 - \frac{1}{4} }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
9. \(\dfrac{y^{1}}{y^{\frac{-5}{3}}}\\= y^{ 1 - (\frac{-5}{3}) }= y^{\frac{8}{3}}\\=\sqrt[3]{ y^{8} }=y^{2}.\sqrt[3]{ y^{2} }\\---------------\)
10. \(\dfrac{x^{\frac{1}{5}}}{x^{\frac{1}{5}}}\\= x^{ \frac{1}{5} - \frac{1}{5} }= x^{0}\\=1\\---------------\)
11. \(\dfrac{x^{1}}{x^{\frac{-1}{4}}}\\= x^{ 1 - (\frac{-1}{4}) }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
12. \(\dfrac{y^{\frac{1}{6}}}{y^{\frac{4}{3}}}\\= y^{ \frac{1}{6} - \frac{4}{3} }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)