Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{1}{3}}}{x^{2}}\\= x^{ \frac{1}{3} - 2 }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
2. \(\dfrac{q^{\frac{5}{4}}}{q^{-2}}\\= q^{ \frac{5}{4} - (-2) }= q^{\frac{13}{4}}\\=\sqrt[4]{ q^{13} }=|q^{3}|.\sqrt[4]{ q }\\---------------\)
3. \(\dfrac{y^{\frac{5}{4}}}{y^{\frac{3}{2}}}\\= y^{ \frac{5}{4} - \frac{3}{2} }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
4. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{5}{3}}}\\= y^{ \frac{-1}{3} - \frac{5}{3} }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
5. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{-5}{4}}}\\= q^{ \frac{1}{4} - (\frac{-5}{4}) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
6. \(\dfrac{a^{1}}{a^{\frac{-1}{3}}}\\= a^{ 1 - (\frac{-1}{3}) }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
7. \(\dfrac{q^{\frac{-4}{3}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{-4}{3} - (\frac{-1}{5}) }= q^{\frac{-17}{15}}\\=\frac{1}{\sqrt[15]{ q^{17} }}\\=\frac{1}{q.\sqrt[15]{ q^{2} }}=\frac{1}{q.\sqrt[15]{ q^{2} }} \color{purple}{\frac{\sqrt[15]{ q^{13} }}{\sqrt[15]{ q^{13} }}} \\=\frac{\sqrt[15]{ q^{13} }}{q^{2}}\\---------------\)
8. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{-5}{3}}}\\= x^{ \frac{4}{5} - (\frac{-5}{3}) }= x^{\frac{37}{15}}\\=\sqrt[15]{ x^{37} }=x^{2}.\sqrt[15]{ x^{7} }\\---------------\)
9. \(\dfrac{y^{\frac{-1}{4}}}{y^{\frac{5}{6}}}\\= y^{ \frac{-1}{4} - \frac{5}{6} }= y^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ y^{13} }}\\=\frac{1}{|y|.\sqrt[12]{ y }}=\frac{1}{|y|.\sqrt[12]{ y }} \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y^{2}|}\\---------------\)
10. \(\dfrac{x^{-1}}{x^{\frac{-5}{2}}}\\= x^{ -1 - (\frac{-5}{2}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
11. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{-4}{5} - (\frac{-3}{5}) }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)
12. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-5}{3}}}\\= x^{ \frac{-1}{3} - (\frac{-5}{3}) }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)