Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{5}{4}}}{x^{-2}}\\= x^{ \frac{5}{4} - (-2) }= x^{\frac{13}{4}}\\=\sqrt[4]{ x^{13} }=|x^{3}|.\sqrt[4]{ x }\\---------------\)
2. \(\dfrac{x^{-1}}{x^{1}}\\= x^{ -1 - 1 }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
3. \(\dfrac{q^{-1}}{q^{\frac{-1}{6}}}\\= q^{ -1 - (\frac{-1}{6}) }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
4. \(\dfrac{x^{1}}{x^{\frac{-5}{3}}}\\= x^{ 1 - (\frac{-5}{3}) }= x^{\frac{8}{3}}\\=\sqrt[3]{ x^{8} }=x^{2}.\sqrt[3]{ x^{2} }\\---------------\)
5. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-1}{2} - (\frac{-1}{2}) }= a^{0}\\=1\\---------------\)
6. \(\dfrac{x^{\frac{-3}{4}}}{x^{-1}}\\= x^{ \frac{-3}{4} - (-1) }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
7. \(\dfrac{q^{\frac{-4}{5}}}{q^{\frac{1}{3}}}\\= q^{ \frac{-4}{5} - \frac{1}{3} }= q^{\frac{-17}{15}}\\=\frac{1}{\sqrt[15]{ q^{17} }}\\=\frac{1}{q.\sqrt[15]{ q^{2} }}=\frac{1}{q.\sqrt[15]{ q^{2} }} \color{purple}{\frac{\sqrt[15]{ q^{13} }}{\sqrt[15]{ q^{13} }}} \\=\frac{\sqrt[15]{ q^{13} }}{q^{2}}\\---------------\)
8. \(\dfrac{y^{\frac{3}{2}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{3}{2} - (\frac{-4}{3}) }= y^{\frac{17}{6}}\\=\sqrt[6]{ y^{17} }=|y^{2}|.\sqrt[6]{ y^{5} }\\---------------\)
9. \(\dfrac{y^{1}}{y^{\frac{-1}{2}}}\\= y^{ 1 - (\frac{-1}{2}) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
10. \(\dfrac{y^{-1}}{y^{-1}}\\= y^{ -1 - (-1) }= y^{0}\\=1\\---------------\)
11. \(\dfrac{x^{1}}{x^{\frac{1}{2}}}\\= x^{ 1 - \frac{1}{2} }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
12. \(\dfrac{x^{\frac{-1}{5}}}{x^{\frac{-2}{5}}}\\= x^{ \frac{-1}{5} - (\frac{-2}{5}) }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)