Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{3}{2}}}{y^{\frac{2}{3}}}\\= y^{ \frac{3}{2} - \frac{2}{3} }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
2. \(\dfrac{q^{1}}{q^{\frac{1}{2}}}\\= q^{ 1 - \frac{1}{2} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
3. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-1}{3} - \frac{1}{2} }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
4. \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-5}{2} - \frac{1}{3} }= x^{\frac{-17}{6}}\\=\frac{1}{\sqrt[6]{ x^{17} }}\\=\frac{1}{|x^{2}|.\sqrt[6]{ x^{5} }}=\frac{1}{|x^{2}|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{3}|}\\---------------\)
5. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{-3}{2}}}\\= x^{ \frac{-2}{3} - (\frac{-3}{2}) }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
6. \(\dfrac{q^{2}}{q^{\frac{4}{3}}}\\= q^{ 2 - \frac{4}{3} }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
7. \(\dfrac{y^{\frac{3}{5}}}{y^{-1}}\\= y^{ \frac{3}{5} - (-1) }= y^{\frac{8}{5}}\\=\sqrt[5]{ y^{8} }=y.\sqrt[5]{ y^{3} }\\---------------\)
8. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{1}{3}}}\\= y^{ \frac{1}{2} - \frac{1}{3} }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
9. \(\dfrac{y^{1}}{y^{\frac{2}{3}}}\\= y^{ 1 - \frac{2}{3} }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
10. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{1}{2}}}\\= y^{ \frac{2}{3} - \frac{1}{2} }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
11. \(\dfrac{y^{\frac{-1}{4}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-1}{4} - \frac{1}{3} }= y^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ y^{7} }}=\frac{1}{\sqrt[12]{ y^{7} }}. \color{purple}{\frac{\sqrt[12]{ y^{5} }}{\sqrt[12]{ y^{5} }}} \\=\frac{\sqrt[12]{ y^{5} }}{|y|}\\---------------\)
12. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-3}{4}}}\\= y^{ \frac{1}{2} - (\frac{-3}{4}) }= y^{\frac{5}{4}}\\=\sqrt[4]{ y^{5} }=|y|.\sqrt[4]{ y }\\---------------\)