Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-4}{3} - (\frac{-1}{2}) }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
2. \(\dfrac{q^{\frac{5}{4}}}{q^{-1}}\\= q^{ \frac{5}{4} - (-1) }= q^{\frac{9}{4}}\\=\sqrt[4]{ q^{9} }=|q^{2}|.\sqrt[4]{ q }\\---------------\)
3. \(\dfrac{q^{1}}{q^{\frac{1}{4}}}\\= q^{ 1 - \frac{1}{4} }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
4. \(\dfrac{x^{-1}}{x^{\frac{-3}{4}}}\\= x^{ -1 - (\frac{-3}{4}) }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
5. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{-5}{6}}}\\= y^{ \frac{5}{2} - (\frac{-5}{6}) }= y^{\frac{10}{3}}\\=\sqrt[3]{ y^{10} }=y^{3}.\sqrt[3]{ y }\\---------------\)
6. \(\dfrac{a^{\frac{-2}{5}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{-2}{5} - (\frac{-4}{5}) }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
7. \(\dfrac{a^{\frac{-5}{4}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{-5}{4} - (\frac{-5}{4}) }= a^{0}\\=1\\---------------\)
8. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{-1}{6} - (\frac{-5}{3}) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
9. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{-3}{4} - (\frac{-4}{5}) }= q^{\frac{1}{20}}\\=\sqrt[20]{ q }\\---------------\)
10. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{1}{4}}}\\= q^{ \frac{-1}{3} - \frac{1}{4} }= q^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ q^{7} }}=\frac{1}{\sqrt[12]{ q^{7} }}. \color{purple}{\frac{\sqrt[12]{ q^{5} }}{\sqrt[12]{ q^{5} }}} \\=\frac{\sqrt[12]{ q^{5} }}{|q|}\\---------------\)
11. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-2}{3} - \frac{2}{3} }= y^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ y^{4} }}\\=\frac{1}{y.\sqrt[3]{ y }}=\frac{1}{y.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{2}}\\---------------\)
12. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{5}{3}}}\\= x^{ \frac{5}{3} - \frac{5}{3} }= x^{0}\\=1\\---------------\)