Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{5}{6}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{5}{6} - (\frac{-1}{2}) }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
2. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{1}{2}}}\\= y^{ \frac{2}{3} - \frac{1}{2} }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
3. \(\dfrac{q^{\frac{-1}{5}}}{q^{1}}\\= q^{ \frac{-1}{5} - 1 }= q^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ q^{6} }}\\=\frac{1}{q.\sqrt[5]{ q }}=\frac{1}{q.\sqrt[5]{ q }} \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q^{2}}\\---------------\)
4. \(\dfrac{y^{\frac{1}{6}}}{y^{\frac{3}{4}}}\\= y^{ \frac{1}{6} - \frac{3}{4} }= y^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ y^{7} }}=\frac{1}{\sqrt[12]{ y^{7} }}. \color{purple}{\frac{\sqrt[12]{ y^{5} }}{\sqrt[12]{ y^{5} }}} \\=\frac{\sqrt[12]{ y^{5} }}{|y|}\\---------------\)
5. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{3}{4}}}\\= a^{ \frac{1}{2} - \frac{3}{4} }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
6. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{2}{5}}}\\= y^{ \frac{-1}{3} - \frac{2}{5} }= y^{\frac{-11}{15}}\\=\frac{1}{\sqrt[15]{ y^{11} }}=\frac{1}{\sqrt[15]{ y^{11} }}. \color{purple}{\frac{\sqrt[15]{ y^{4} }}{\sqrt[15]{ y^{4} }}} \\=\frac{\sqrt[15]{ y^{4} }}{y}\\---------------\)
7. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-3}{2} - \frac{1}{2} }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
8. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-2}{3} - (\frac{-1}{2}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
9. \(\dfrac{a^{\frac{-5}{4}}}{a^{\frac{5}{3}}}\\= a^{ \frac{-5}{4} - \frac{5}{3} }= a^{\frac{-35}{12}}\\=\frac{1}{\sqrt[12]{ a^{35} }}\\=\frac{1}{|a^{2}|.\sqrt[12]{ a^{11} }}=\frac{1}{|a^{2}|.\sqrt[12]{ a^{11} }} \color{purple}{\frac{\sqrt[12]{ a }}{\sqrt[12]{ a }}} \\=\frac{\sqrt[12]{ a }}{|a^{3}|}\\---------------\)
10. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{-3}{4}}}\\= y^{ \frac{5}{2} - (\frac{-3}{4}) }= y^{\frac{13}{4}}\\=\sqrt[4]{ y^{13} }=|y^{3}|.\sqrt[4]{ y }\\---------------\)
11. \(\dfrac{a^{1}}{a^{\frac{-5}{2}}}\\= a^{ 1 - (\frac{-5}{2}) }= a^{\frac{7}{2}}\\= \sqrt{ a^{7} } =|a^{3}|. \sqrt{ a } \\---------------\)
12. \(\dfrac{x^{\frac{3}{5}}}{x^{-1}}\\= x^{ \frac{3}{5} - (-1) }= x^{\frac{8}{5}}\\=\sqrt[5]{ x^{8} }=x.\sqrt[5]{ x^{3} }\\---------------\)