Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-3}{5} - \frac{1}{3} }= x^{\frac{-14}{15}}\\=\frac{1}{\sqrt[15]{ x^{14} }}=\frac{1}{\sqrt[15]{ x^{14} }}. \color{purple}{\frac{\sqrt[15]{ x }}{\sqrt[15]{ x }}} \\=\frac{\sqrt[15]{ x }}{x}\\---------------\)
2. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-2}{3} - (\frac{-1}{3}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
3. \(\dfrac{x^{2}}{x^{\frac{1}{3}}}\\= x^{ 2 - \frac{1}{3} }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)
4. \(\dfrac{a^{\frac{-4}{5}}}{a^{\frac{5}{3}}}\\= a^{ \frac{-4}{5} - \frac{5}{3} }= a^{\frac{-37}{15}}\\=\frac{1}{\sqrt[15]{ a^{37} }}\\=\frac{1}{a^{2}.\sqrt[15]{ a^{7} }}=\frac{1}{a^{2}.\sqrt[15]{ a^{7} }} \color{purple}{\frac{\sqrt[15]{ a^{8} }}{\sqrt[15]{ a^{8} }}} \\=\frac{\sqrt[15]{ a^{8} }}{a^{3}}\\---------------\)
5. \(\dfrac{y^{-1}}{y^{\frac{-2}{3}}}\\= y^{ -1 - (\frac{-2}{3}) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
6. \(\dfrac{y^{\frac{5}{6}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{5}{6} - (\frac{-2}{3}) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
7. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-4}{5}}}\\= y^{ \frac{-1}{2} - (\frac{-4}{5}) }= y^{\frac{3}{10}}\\=\sqrt[10]{ y^{3} }\\---------------\)
8. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{5}{3}}}\\= x^{ \frac{2}{3} - \frac{5}{3} }= x^{-1}\\=\frac{1}{x}\\---------------\)
9. \(\dfrac{q^{\frac{-2}{5}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{-2}{5} - (\frac{-2}{3}) }= q^{\frac{4}{15}}\\=\sqrt[15]{ q^{4} }\\---------------\)
10. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-1}{4}}}\\= a^{ \frac{1}{2} - (\frac{-1}{4}) }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
11. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{-3}{5} - (\frac{-5}{4}) }= x^{\frac{13}{20}}\\=\sqrt[20]{ x^{13} }\\---------------\)
12. \(\dfrac{x^{\frac{1}{3}}}{x^{1}}\\= x^{ \frac{1}{3} - 1 }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)