Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{-1}}{x^{\frac{-1}{4}}}\\= x^{ -1 - (\frac{-1}{4}) }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
2. \(\dfrac{y^{2}}{y^{\frac{-3}{2}}}\\= y^{ 2 - (\frac{-3}{2}) }= y^{\frac{7}{2}}\\= \sqrt{ y^{7} } =|y^{3}|. \sqrt{ y } \\---------------\)
3. \(\dfrac{q^{\frac{2}{3}}}{q^{1}}\\= q^{ \frac{2}{3} - 1 }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
4. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{2}{3} - (\frac{-1}{2}) }= a^{\frac{7}{6}}\\=\sqrt[6]{ a^{7} }=|a|.\sqrt[6]{ a }\\---------------\)
5. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{-1}{4}}}\\= x^{ \frac{4}{5} - (\frac{-1}{4}) }= x^{\frac{21}{20}}\\=\sqrt[20]{ x^{21} }=|x|.\sqrt[20]{ x }\\---------------\)
6. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{-3}{4} - (\frac{-5}{4}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
7. \(\dfrac{a^{\frac{3}{4}}}{a^{\frac{-3}{2}}}\\= a^{ \frac{3}{4} - (\frac{-3}{2}) }= a^{\frac{9}{4}}\\=\sqrt[4]{ a^{9} }=|a^{2}|.\sqrt[4]{ a }\\---------------\)
8. \(\dfrac{a^{\frac{-5}{4}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-5}{4} - (\frac{-1}{3}) }= a^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ a^{11} }}=\frac{1}{\sqrt[12]{ a^{11} }}. \color{purple}{\frac{\sqrt[12]{ a }}{\sqrt[12]{ a }}} \\=\frac{\sqrt[12]{ a }}{|a|}\\---------------\)
9. \(\dfrac{a^{\frac{4}{3}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{4}{3} - (\frac{-2}{5}) }= a^{\frac{26}{15}}\\=\sqrt[15]{ a^{26} }=a.\sqrt[15]{ a^{11} }\\---------------\)
10. \(\dfrac{q^{1}}{q^{\frac{-5}{6}}}\\= q^{ 1 - (\frac{-5}{6}) }= q^{\frac{11}{6}}\\=\sqrt[6]{ q^{11} }=|q|.\sqrt[6]{ q^{5} }\\---------------\)
11. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-4}{3}}}\\= a^{ \frac{1}{2} - (\frac{-4}{3}) }= a^{\frac{11}{6}}\\=\sqrt[6]{ a^{11} }=|a|.\sqrt[6]{ a^{5} }\\---------------\)
12. \(\dfrac{y^{-1}}{y^{-1}}\\= y^{ -1 - (-1) }= y^{0}\\=1\\---------------\)