Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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