Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{-4}{5}}}\\= y^{ \frac{-2}{3} - (\frac{-4}{5}) }= y^{\frac{2}{15}}\\=\sqrt[15]{ y^{2} }\\---------------\)
2. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{-1}{2} - (\frac{-5}{2}) }= q^{2}\\\\---------------\)
3. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-1}{5} - \frac{1}{3} }= y^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ y^{8} }}=\frac{1}{\sqrt[15]{ y^{8} }}. \color{purple}{\frac{\sqrt[15]{ y^{7} }}{\sqrt[15]{ y^{7} }}} \\=\frac{\sqrt[15]{ y^{7} }}{y}\\---------------\)
4. \(\dfrac{a^{-1}}{a^{\frac{-5}{2}}}\\= a^{ -1 - (\frac{-5}{2}) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
5. \(\dfrac{y^{\frac{5}{6}}}{y^{\frac{-1}{4}}}\\= y^{ \frac{5}{6} - (\frac{-1}{4}) }= y^{\frac{13}{12}}\\=\sqrt[12]{ y^{13} }=|y|.\sqrt[12]{ y }\\---------------\)
6. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-1}{6}}}\\= x^{ \frac{-1}{2} - (\frac{-1}{6}) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
7. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{4}{3} - (\frac{-1}{2}) }= y^{\frac{11}{6}}\\=\sqrt[6]{ y^{11} }=|y|.\sqrt[6]{ y^{5} }\\---------------\)
8. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{-1}{4}}}\\= y^{ \frac{-2}{3} - (\frac{-1}{4}) }= y^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ y^{5} }}=\frac{1}{\sqrt[12]{ y^{5} }}. \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y|}\\---------------\)
9. \(\dfrac{a^{\frac{1}{5}}}{a^{1}}\\= a^{ \frac{1}{5} - 1 }= a^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ a^{4} }}=\frac{1}{\sqrt[5]{ a^{4} }}. \color{purple}{\frac{\sqrt[5]{ a }}{\sqrt[5]{ a }}} \\=\frac{\sqrt[5]{ a }}{a}\\---------------\)
10. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{2}{5}}}\\= x^{ \frac{1}{3} - \frac{2}{5} }= x^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ x }}=\frac{1}{\sqrt[15]{ x }}. \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x}\\---------------\)
11. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{-2}{3} - (\frac{-3}{5}) }= y^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ y }}=\frac{1}{\sqrt[15]{ y }}. \color{purple}{\frac{\sqrt[15]{ y^{14} }}{\sqrt[15]{ y^{14} }}} \\=\frac{\sqrt[15]{ y^{14} }}{y}\\---------------\)
12. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{4}{5}}}\\= q^{ \frac{-2}{3} - \frac{4}{5} }= q^{\frac{-22}{15}}\\=\frac{1}{\sqrt[15]{ q^{22} }}\\=\frac{1}{q.\sqrt[15]{ q^{7} }}=\frac{1}{q.\sqrt[15]{ q^{7} }} \color{purple}{\frac{\sqrt[15]{ q^{8} }}{\sqrt[15]{ q^{8} }}} \\=\frac{\sqrt[15]{ q^{8} }}{q^{2}}\\---------------\)