Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{3}{2}}}{y^{\frac{3}{2}}}\\= y^{ \frac{3}{2} - \frac{3}{2} }= y^{0}\\=1\\---------------\)
2. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{-2}{3} - (\frac{-4}{5}) }= q^{\frac{2}{15}}\\=\sqrt[15]{ q^{2} }\\---------------\)
3. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{-3}{2}}}\\= x^{ \frac{5}{3} - (\frac{-3}{2}) }= x^{\frac{19}{6}}\\=\sqrt[6]{ x^{19} }=|x^{3}|.\sqrt[6]{ x }\\---------------\)
4. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{-1}{3} - (\frac{-2}{5}) }= q^{\frac{1}{15}}\\=\sqrt[15]{ q }\\---------------\)
5. \(\dfrac{y^{\frac{2}{5}}}{y^{2}}\\= y^{ \frac{2}{5} - 2 }= y^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ y^{8} }}\\=\frac{1}{y.\sqrt[5]{ y^{3} }}=\frac{1}{y.\sqrt[5]{ y^{3} }} \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y^{2}}\\---------------\)
6. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{3}{2}}}\\= a^{ \frac{1}{3} - \frac{3}{2} }= a^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ a^{7} }}\\=\frac{1}{|a|.\sqrt[6]{ a }}=\frac{1}{|a|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{2}|}\\---------------\)
7. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{1}{2} - (\frac{-1}{2}) }= y^{1}\\\\---------------\)
8. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-1}{2} - (\frac{-1}{2}) }= x^{0}\\=1\\---------------\)
9. \(\dfrac{q^{\frac{-4}{3}}}{q^{\frac{5}{6}}}\\= q^{ \frac{-4}{3} - \frac{5}{6} }= q^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ q^{13} }}\\=\frac{1}{|q^{2}|.\sqrt[6]{ q }}=\frac{1}{|q^{2}|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{3}|}\\---------------\)
10. \(\dfrac{a^{\frac{-4}{3}}}{a^{1}}\\= a^{ \frac{-4}{3} - 1 }= a^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ a^{7} }}\\=\frac{1}{a^{2}.\sqrt[3]{ a }}=\frac{1}{a^{2}.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{3}}\\---------------\)
11. \(\dfrac{y^{\frac{1}{2}}}{y^{-2}}\\= y^{ \frac{1}{2} - (-2) }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)
12. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{3}{2}}}\\= q^{ \frac{-1}{2} - \frac{3}{2} }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)