Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{1}{5}}}\\= y^{ \frac{1}{2} - \frac{1}{5} }= y^{\frac{3}{10}}\\=\sqrt[10]{ y^{3} }\\---------------\)
2. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{-1}{3} - (\frac{-1}{3}) }= x^{0}\\=1\\---------------\)
3. \(\dfrac{a^{\frac{3}{2}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{3}{2} - (\frac{-5}{6}) }= a^{\frac{7}{3}}\\=\sqrt[3]{ a^{7} }=a^{2}.\sqrt[3]{ a }\\---------------\)
4. \(\dfrac{x^{1}}{x^{\frac{-5}{3}}}\\= x^{ 1 - (\frac{-5}{3}) }= x^{\frac{8}{3}}\\=\sqrt[3]{ x^{8} }=x^{2}.\sqrt[3]{ x^{2} }\\---------------\)
5. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{4}{5}}}\\= x^{ \frac{3}{5} - \frac{4}{5} }= x^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ x }}=\frac{1}{\sqrt[5]{ x }}. \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x}\\---------------\)
6. \(\dfrac{q^{1}}{q^{\frac{1}{5}}}\\= q^{ 1 - \frac{1}{5} }= q^{\frac{4}{5}}\\=\sqrt[5]{ q^{4} }\\---------------\)
7. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{-5}{6}}}\\= y^{ \frac{-5}{4} - (\frac{-5}{6}) }= y^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ y^{5} }}=\frac{1}{\sqrt[12]{ y^{5} }}. \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y|}\\---------------\)
8. \(\dfrac{x^{1}}{x^{\frac{-1}{2}}}\\= x^{ 1 - (\frac{-1}{2}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
9. \(\dfrac{y^{\frac{-3}{2}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{-3}{2} - (\frac{-1}{3}) }= y^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[6]{ y }}=\frac{1}{|y|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{2}|}\\---------------\)
10. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-4}{3} - (\frac{-1}{2}) }= x^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ x^{5} }}=\frac{1}{\sqrt[6]{ x^{5} }}. \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x|}\\---------------\)
11. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{3}{4}}}\\= a^{ \frac{-1}{2} - \frac{3}{4} }= a^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ a^{5} }}\\=\frac{1}{|a|.\sqrt[4]{ a }}=\frac{1}{|a|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{2}|}\\---------------\)
12. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{-1}{5} - (\frac{-4}{3}) }= y^{\frac{17}{15}}\\=\sqrt[15]{ y^{17} }=y.\sqrt[15]{ y^{2} }\\---------------\)