Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{1}{2}}}\\= a^{ \frac{1}{4} - \frac{1}{2} }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
2. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{3}{4} - (\frac{-1}{2}) }= y^{\frac{5}{4}}\\=\sqrt[4]{ y^{5} }=|y|.\sqrt[4]{ y }\\---------------\)
3. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{3}{5} - (\frac{-5}{6}) }= a^{\frac{43}{30}}\\=\sqrt[30]{ a^{43} }=|a|.\sqrt[30]{ a^{13} }\\---------------\)
4. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-1}{2} - \frac{1}{3} }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
5. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{4}{5} - (\frac{-3}{5}) }= x^{\frac{7}{5}}\\=\sqrt[5]{ x^{7} }=x.\sqrt[5]{ x^{2} }\\---------------\)
6. \(\dfrac{x^{-1}}{x^{1}}\\= x^{ -1 - 1 }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
7. \(\dfrac{x^{\frac{-5}{4}}}{x^{-1}}\\= x^{ \frac{-5}{4} - (-1) }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
8. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{1}{5}}}\\= q^{ \frac{2}{3} - \frac{1}{5} }= q^{\frac{7}{15}}\\=\sqrt[15]{ q^{7} }\\---------------\)
9. \(\dfrac{q^{\frac{5}{2}}}{q^{\frac{2}{3}}}\\= q^{ \frac{5}{2} - \frac{2}{3} }= q^{\frac{11}{6}}\\=\sqrt[6]{ q^{11} }=|q|.\sqrt[6]{ q^{5} }\\---------------\)
10. \(\dfrac{x^{1}}{x^{1}}\\= x^{ 1 - 1 }= x^{0}\\=1\\---------------\)
11. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-2}{5} - \frac{1}{3} }= x^{\frac{-11}{15}}\\=\frac{1}{\sqrt[15]{ x^{11} }}=\frac{1}{\sqrt[15]{ x^{11} }}. \color{purple}{\frac{\sqrt[15]{ x^{4} }}{\sqrt[15]{ x^{4} }}} \\=\frac{\sqrt[15]{ x^{4} }}{x}\\---------------\)
12. \(\dfrac{y^{\frac{3}{2}}}{y^{\frac{3}{2}}}\\= y^{ \frac{3}{2} - \frac{3}{2} }= y^{0}\\=1\\---------------\)