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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{-5}{6}}}\\= y^{ \frac{2}{3} - (\frac{-5}{6}) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
2. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{3}{2}}}\\= y^{ \frac{-5}{4} - \frac{3}{2} }= y^{\frac{-11}{4}}\\=\frac{1}{\sqrt[4]{ y^{11} }}\\=\frac{1}{|y^{2}|.\sqrt[4]{ y^{3} }}=\frac{1}{|y^{2}|.\sqrt[4]{ y^{3} }} \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y^{3}|}\\---------------\)
3. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{5}{6} - (\frac{-1}{2}) }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
4. \(\dfrac{a^{-1}}{a^{\frac{2}{3}}}\\= a^{ -1 - \frac{2}{3} }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
5. \(\dfrac{x^{\frac{-3}{4}}}{x^{\frac{3}{2}}}\\= x^{ \frac{-3}{4} - \frac{3}{2} }= x^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ x^{9} }}\\=\frac{1}{|x^{2}|.\sqrt[4]{ x }}=\frac{1}{|x^{2}|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{3}|}\\---------------\)
6. \(\dfrac{y^{\frac{3}{2}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{3}{2} - (\frac{-2}{3}) }= y^{\frac{13}{6}}\\=\sqrt[6]{ y^{13} }=|y^{2}|.\sqrt[6]{ y }\\---------------\)
7. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{1}{3}}}\\= a^{ \frac{1}{2} - \frac{1}{3} }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
8. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{-3}{2} - (\frac{-1}{6}) }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
9. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{5}{3} - (\frac{-2}{5}) }= q^{\frac{31}{15}}\\=\sqrt[15]{ q^{31} }=q^{2}.\sqrt[15]{ q }\\---------------\)
10. \(\dfrac{y^{1}}{y^{\frac{-5}{3}}}\\= y^{ 1 - (\frac{-5}{3}) }= y^{\frac{8}{3}}\\=\sqrt[3]{ y^{8} }=y^{2}.\sqrt[3]{ y^{2} }\\---------------\)
11. \(\dfrac{q^{\frac{-4}{3}}}{q^{\frac{5}{2}}}\\= q^{ \frac{-4}{3} - \frac{5}{2} }= q^{\frac{-23}{6}}\\=\frac{1}{\sqrt[6]{ q^{23} }}\\=\frac{1}{|q^{3}|.\sqrt[6]{ q^{5} }}=\frac{1}{|q^{3}|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{4}|}\\---------------\)
12. \(\dfrac{a^{\frac{-1}{6}}}{a^{-1}}\\= a^{ \frac{-1}{6} - (-1) }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)