Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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