Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{5}{4}}}\\= y^{ \frac{-2}{3} - \frac{5}{4} }= y^{\frac{-23}{12}}\\=\frac{1}{\sqrt[12]{ y^{23} }}\\=\frac{1}{|y|.\sqrt[12]{ y^{11} }}=\frac{1}{|y|.\sqrt[12]{ y^{11} }} \color{purple}{\frac{\sqrt[12]{ y }}{\sqrt[12]{ y }}} \\=\frac{\sqrt[12]{ y }}{|y^{2}|}\\---------------\)
2. \(\dfrac{a^{\frac{-5}{6}}}{a^{\frac{-3}{2}}}\\= a^{ \frac{-5}{6} - (\frac{-3}{2}) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
3. \(\dfrac{x^{\frac{-3}{5}}}{x^{1}}\\= x^{ \frac{-3}{5} - 1 }= x^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ x^{8} }}\\=\frac{1}{x.\sqrt[5]{ x^{3} }}=\frac{1}{x.\sqrt[5]{ x^{3} }} \color{purple}{\frac{\sqrt[5]{ x^{2} }}{\sqrt[5]{ x^{2} }}} \\=\frac{\sqrt[5]{ x^{2} }}{x^{2}}\\---------------\)
4. \(\dfrac{y^{\frac{-5}{6}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-5}{6} - \frac{1}{3} }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
5. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-4}{5} - \frac{1}{2} }= y^{\frac{-13}{10}}\\=\frac{1}{\sqrt[10]{ y^{13} }}\\=\frac{1}{|y|.\sqrt[10]{ y^{3} }}=\frac{1}{|y|.\sqrt[10]{ y^{3} }} \color{purple}{\frac{\sqrt[10]{ y^{7} }}{\sqrt[10]{ y^{7} }}} \\=\frac{\sqrt[10]{ y^{7} }}{|y^{2}|}\\---------------\)
6. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{3}{5}}}\\= x^{ \frac{-1}{3} - \frac{3}{5} }= x^{\frac{-14}{15}}\\=\frac{1}{\sqrt[15]{ x^{14} }}=\frac{1}{\sqrt[15]{ x^{14} }}. \color{purple}{\frac{\sqrt[15]{ x }}{\sqrt[15]{ x }}} \\=\frac{\sqrt[15]{ x }}{x}\\---------------\)
7. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{1}{2} - (\frac{-1}{6}) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
8. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-5}{3} - \frac{1}{3} }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
9. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{4}{5}}}\\= a^{ \frac{1}{2} - \frac{4}{5} }= a^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ a^{3} }}=\frac{1}{\sqrt[10]{ a^{3} }}. \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a|}\\---------------\)
10. \(\dfrac{q^{\frac{-2}{5}}}{q^{2}}\\= q^{ \frac{-2}{5} - 2 }= q^{\frac{-12}{5}}\\=\frac{1}{\sqrt[5]{ q^{12} }}\\=\frac{1}{q^{2}.\sqrt[5]{ q^{2} }}=\frac{1}{q^{2}.\sqrt[5]{ q^{2} }} \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q^{3}}\\---------------\)
11. \(\dfrac{y^{\frac{-1}{6}}}{y^{-2}}\\= y^{ \frac{-1}{6} - (-2) }= y^{\frac{11}{6}}\\=\sqrt[6]{ y^{11} }=|y|.\sqrt[6]{ y^{5} }\\---------------\)
12. \(\dfrac{x^{\frac{5}{6}}}{x^{\frac{1}{6}}}\\= x^{ \frac{5}{6} - \frac{1}{6} }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)