Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{2}{5} - (\frac{-3}{5}) }= a^{1}\\\\---------------\)
2. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{-1}{4}}}\\= y^{ \frac{-2}{3} - (\frac{-1}{4}) }= y^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ y^{5} }}=\frac{1}{\sqrt[12]{ y^{5} }}. \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y|}\\---------------\)
3. \(\dfrac{q^{\frac{-2}{3}}}{q^{2}}\\= q^{ \frac{-2}{3} - 2 }= q^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ q^{8} }}\\=\frac{1}{q^{2}.\sqrt[3]{ q^{2} }}=\frac{1}{q^{2}.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{3}}\\---------------\)
4. \(\dfrac{a^{\frac{1}{6}}}{a^{-1}}\\= a^{ \frac{1}{6} - (-1) }= a^{\frac{7}{6}}\\=\sqrt[6]{ a^{7} }=|a|.\sqrt[6]{ a }\\---------------\)
5. \(\dfrac{q^{\frac{-4}{3}}}{q^{\frac{5}{3}}}\\= q^{ \frac{-4}{3} - \frac{5}{3} }= q^{-3}\\=\frac{1}{q^{3}}\\---------------\)
6. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{-3}{5} - (\frac{-1}{3}) }= y^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ y^{4} }}=\frac{1}{\sqrt[15]{ y^{4} }}. \color{purple}{\frac{\sqrt[15]{ y^{11} }}{\sqrt[15]{ y^{11} }}} \\=\frac{\sqrt[15]{ y^{11} }}{y}\\---------------\)
7. \(\dfrac{x^{\frac{1}{4}}}{x^{\frac{4}{3}}}\\= x^{ \frac{1}{4} - \frac{4}{3} }= x^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ x^{13} }}\\=\frac{1}{|x|.\sqrt[12]{ x }}=\frac{1}{|x|.\sqrt[12]{ x }} \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x^{2}|}\\---------------\)
8. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{1}{3} - (\frac{-4}{5}) }= a^{\frac{17}{15}}\\=\sqrt[15]{ a^{17} }=a.\sqrt[15]{ a^{2} }\\---------------\)
9. \(\dfrac{x^{-1}}{x^{1}}\\= x^{ -1 - 1 }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
10. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{2}{3} - (\frac{-2}{3}) }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
11. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-5}{4} - \frac{2}{3} }= y^{\frac{-23}{12}}\\=\frac{1}{\sqrt[12]{ y^{23} }}\\=\frac{1}{|y|.\sqrt[12]{ y^{11} }}=\frac{1}{|y|.\sqrt[12]{ y^{11} }} \color{purple}{\frac{\sqrt[12]{ y }}{\sqrt[12]{ y }}} \\=\frac{\sqrt[12]{ y }}{|y^{2}|}\\---------------\)
12. \(\dfrac{x^{2}}{x^{\frac{-2}{5}}}\\= x^{ 2 - (\frac{-2}{5}) }= x^{\frac{12}{5}}\\=\sqrt[5]{ x^{12} }=x^{2}.\sqrt[5]{ x^{2} }\\---------------\)