Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{5}{6}}}\\= y^{ \frac{2}{3} - \frac{5}{6} }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
2. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-1}{3} - \frac{2}{3} }= y^{-1}\\=\frac{1}{y}\\---------------\)
3. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{1}{5}}}\\= q^{ \frac{1}{3} - \frac{1}{5} }= q^{\frac{2}{15}}\\=\sqrt[15]{ q^{2} }\\---------------\)
4. \(\dfrac{y^{\frac{2}{5}}}{y^{2}}\\= y^{ \frac{2}{5} - 2 }= y^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ y^{8} }}\\=\frac{1}{y.\sqrt[5]{ y^{3} }}=\frac{1}{y.\sqrt[5]{ y^{3} }} \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y^{2}}\\---------------\)
5. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{2}{5} - (\frac{-2}{3}) }= y^{\frac{16}{15}}\\=\sqrt[15]{ y^{16} }=y.\sqrt[15]{ y }\\---------------\)
6. \(\dfrac{x^{\frac{-5}{6}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-5}{6} - (\frac{-1}{2}) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
7. \(\dfrac{y^{1}}{y^{\frac{5}{6}}}\\= y^{ 1 - \frac{5}{6} }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
8. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{1}{3} - (\frac{-1}{5}) }= q^{\frac{8}{15}}\\=\sqrt[15]{ q^{8} }\\---------------\)
9. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{-2}{5} - (\frac{-3}{4}) }= x^{\frac{7}{20}}\\=\sqrt[20]{ x^{7} }\\---------------\)
10. \(\dfrac{q^{\frac{3}{5}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{3}{5} - (\frac{-4}{5}) }= q^{\frac{7}{5}}\\=\sqrt[5]{ q^{7} }=q.\sqrt[5]{ q^{2} }\\---------------\)
11. \(\dfrac{q^{\frac{-5}{4}}}{q^{2}}\\= q^{ \frac{-5}{4} - 2 }= q^{\frac{-13}{4}}\\=\frac{1}{\sqrt[4]{ q^{13} }}\\=\frac{1}{|q^{3}|.\sqrt[4]{ q }}=\frac{1}{|q^{3}|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{4}|}\\---------------\)
12. \(\dfrac{q^{\frac{5}{4}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{5}{4} - (\frac{-1}{2}) }= q^{\frac{7}{4}}\\=\sqrt[4]{ q^{7} }=|q|.\sqrt[4]{ q^{3} }\\---------------\)