Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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