Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{2}{5}}}\\= y^{ \frac{-1}{2} - \frac{2}{5} }= y^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ y^{9} }}=\frac{1}{\sqrt[10]{ y^{9} }}. \color{purple}{\frac{\sqrt[10]{ y }}{\sqrt[10]{ y }}} \\=\frac{\sqrt[10]{ y }}{|y|}\\---------------\)
2. \(\dfrac{a^{-1}}{a^{\frac{5}{3}}}\\= a^{ -1 - \frac{5}{3} }= a^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ a^{8} }}\\=\frac{1}{a^{2}.\sqrt[3]{ a^{2} }}=\frac{1}{a^{2}.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{3}}\\---------------\)
3. \(\dfrac{x^{\frac{5}{4}}}{x^{-1}}\\= x^{ \frac{5}{4} - (-1) }= x^{\frac{9}{4}}\\=\sqrt[4]{ x^{9} }=|x^{2}|.\sqrt[4]{ x }\\---------------\)
4. \(\dfrac{y^{-1}}{y^{-1}}\\= y^{ -1 - (-1) }= y^{0}\\=1\\---------------\)
5. \(\dfrac{y^{\frac{3}{2}}}{y^{1}}\\= y^{ \frac{3}{2} - 1 }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
6. \(\dfrac{a^{-1}}{a^{\frac{-5}{6}}}\\= a^{ -1 - (\frac{-5}{6}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
7. \(\dfrac{y^{\frac{5}{3}}}{y^{\frac{3}{4}}}\\= y^{ \frac{5}{3} - \frac{3}{4} }= y^{\frac{11}{12}}\\=\sqrt[12]{ y^{11} }\\---------------\)
8. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{-2}{3} - (\frac{-2}{5}) }= q^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ q^{4} }}=\frac{1}{\sqrt[15]{ q^{4} }}. \color{purple}{\frac{\sqrt[15]{ q^{11} }}{\sqrt[15]{ q^{11} }}} \\=\frac{\sqrt[15]{ q^{11} }}{q}\\---------------\)
9. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{4}{3}}}\\= q^{ \frac{-5}{2} - \frac{4}{3} }= q^{\frac{-23}{6}}\\=\frac{1}{\sqrt[6]{ q^{23} }}\\=\frac{1}{|q^{3}|.\sqrt[6]{ q^{5} }}=\frac{1}{|q^{3}|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{4}|}\\---------------\)
10. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{2}{3} - (\frac{-3}{5}) }= y^{\frac{19}{15}}\\=\sqrt[15]{ y^{19} }=y.\sqrt[15]{ y^{4} }\\---------------\)
11. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{-3}{4} - (\frac{-5}{6}) }= a^{\frac{1}{12}}\\=\sqrt[12]{ a }\\---------------\)
12. \(\dfrac{x^{\frac{5}{6}}}{x^{\frac{4}{3}}}\\= x^{ \frac{5}{6} - \frac{4}{3} }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)