Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{-5}{2} - (\frac{-1}{6}) }= y^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ y^{7} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y }}=\frac{1}{y^{2}.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{3}}\\---------------\)
2. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{-5}{3}}}\\= y^{ \frac{4}{3} - (\frac{-5}{3}) }= y^{3}\\\\---------------\)
3. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{-4}{5}}}\\= y^{ \frac{-4}{3} - (\frac{-4}{5}) }= y^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ y^{8} }}=\frac{1}{\sqrt[15]{ y^{8} }}. \color{purple}{\frac{\sqrt[15]{ y^{7} }}{\sqrt[15]{ y^{7} }}} \\=\frac{\sqrt[15]{ y^{7} }}{y}\\---------------\)
4. \(\dfrac{y^{-1}}{y^{-1}}\\= y^{ -1 - (-1) }= y^{0}\\=1\\---------------\)
5. \(\dfrac{a^{\frac{-3}{5}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-3}{5} - (\frac{-1}{3}) }= a^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ a^{4} }}=\frac{1}{\sqrt[15]{ a^{4} }}. \color{purple}{\frac{\sqrt[15]{ a^{11} }}{\sqrt[15]{ a^{11} }}} \\=\frac{\sqrt[15]{ a^{11} }}{a}\\---------------\)
6. \(\dfrac{q^{\frac{-1}{2}}}{q^{-2}}\\= q^{ \frac{-1}{2} - (-2) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
7. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-1}{4}}}\\= q^{ \frac{1}{3} - (\frac{-1}{4}) }= q^{\frac{7}{12}}\\=\sqrt[12]{ q^{7} }\\---------------\)
8. \(\dfrac{a^{\frac{4}{3}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{4}{3} - (\frac{-1}{2}) }= a^{\frac{11}{6}}\\=\sqrt[6]{ a^{11} }=|a|.\sqrt[6]{ a^{5} }\\---------------\)
9. \(\dfrac{a^{\frac{-5}{2}}}{a^{\frac{2}{5}}}\\= a^{ \frac{-5}{2} - \frac{2}{5} }= a^{\frac{-29}{10}}\\=\frac{1}{\sqrt[10]{ a^{29} }}\\=\frac{1}{|a^{2}|.\sqrt[10]{ a^{9} }}=\frac{1}{|a^{2}|.\sqrt[10]{ a^{9} }} \color{purple}{\frac{\sqrt[10]{ a }}{\sqrt[10]{ a }}} \\=\frac{\sqrt[10]{ a }}{|a^{3}|}\\---------------\)
10. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{-1}{4}}}\\= x^{ \frac{-5}{3} - (\frac{-1}{4}) }= x^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ x^{17} }}\\=\frac{1}{|x|.\sqrt[12]{ x^{5} }}=\frac{1}{|x|.\sqrt[12]{ x^{5} }} \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x^{2}|}\\---------------\)
11. \(\dfrac{a^{\frac{-2}{5}}}{a^{\frac{2}{5}}}\\= a^{ \frac{-2}{5} - \frac{2}{5} }= a^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ a^{4} }}=\frac{1}{\sqrt[5]{ a^{4} }}. \color{purple}{\frac{\sqrt[5]{ a }}{\sqrt[5]{ a }}} \\=\frac{\sqrt[5]{ a }}{a}\\---------------\)
12. \(\dfrac{a^{\frac{1}{6}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{1}{6} - (\frac{-1}{3}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)