Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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