Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{5}{2}}}{q^{-1}}\\= q^{ \frac{5}{2} - (-1) }= q^{\frac{7}{2}}\\= \sqrt{ q^{7} } =|q^{3}|. \sqrt{ q } \\---------------\)
2. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{1}{6}}}\\= y^{ \frac{-2}{3} - \frac{1}{6} }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
3. \(\dfrac{a^{1}}{a^{\frac{1}{2}}}\\= a^{ 1 - \frac{1}{2} }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
4. \(\dfrac{q^{\frac{1}{5}}}{q^{\frac{-3}{4}}}\\= q^{ \frac{1}{5} - (\frac{-3}{4}) }= q^{\frac{19}{20}}\\=\sqrt[20]{ q^{19} }\\---------------\)
5. \(\dfrac{x^{2}}{x^{\frac{-5}{2}}}\\= x^{ 2 - (\frac{-5}{2}) }= x^{\frac{9}{2}}\\= \sqrt{ x^{9} } =|x^{4}|. \sqrt{ x } \\---------------\)
6. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{-3}{4}}}\\= y^{ \frac{2}{5} - (\frac{-3}{4}) }= y^{\frac{23}{20}}\\=\sqrt[20]{ y^{23} }=|y|.\sqrt[20]{ y^{3} }\\---------------\)
7. \(\dfrac{y^{-1}}{y^{\frac{2}{3}}}\\= y^{ -1 - \frac{2}{3} }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
8. \(\dfrac{y^{\frac{-5}{3}}}{y^{1}}\\= y^{ \frac{-5}{3} - 1 }= y^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ y^{8} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }}=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{3}}\\---------------\)
9. \(\dfrac{a^{\frac{1}{6}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{1}{6} - (\frac{-1}{3}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
10. \(\dfrac{y^{-1}}{y^{\frac{-4}{5}}}\\= y^{ -1 - (\frac{-4}{5}) }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)
11. \(\dfrac{x^{1}}{x^{\frac{-1}{2}}}\\= x^{ 1 - (\frac{-1}{2}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
12. \(\dfrac{x^{\frac{1}{3}}}{x^{-1}}\\= x^{ \frac{1}{3} - (-1) }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)