Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{3}{5}}}\\= y^{ \frac{5}{2} - \frac{3}{5} }= y^{\frac{19}{10}}\\=\sqrt[10]{ y^{19} }=|y|.\sqrt[10]{ y^{9} }\\---------------\)
2. \(\dfrac{a^{\frac{5}{4}}}{a^{-1}}\\= a^{ \frac{5}{4} - (-1) }= a^{\frac{9}{4}}\\=\sqrt[4]{ a^{9} }=|a^{2}|.\sqrt[4]{ a }\\---------------\)
3. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{1}{3} - (\frac{-1}{3}) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
4. \(\dfrac{q^{\frac{-4}{5}}}{q^{1}}\\= q^{ \frac{-4}{5} - 1 }= q^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ q^{9} }}\\=\frac{1}{q.\sqrt[5]{ q^{4} }}=\frac{1}{q.\sqrt[5]{ q^{4} }} \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q^{2}}\\---------------\)
5. \(\dfrac{a^{\frac{3}{4}}}{a^{1}}\\= a^{ \frac{3}{4} - 1 }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
6. \(\dfrac{a^{\frac{-2}{5}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-2}{5} - \frac{2}{3} }= a^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ a^{16} }}\\=\frac{1}{a.\sqrt[15]{ a }}=\frac{1}{a.\sqrt[15]{ a }} \color{purple}{\frac{\sqrt[15]{ a^{14} }}{\sqrt[15]{ a^{14} }}} \\=\frac{\sqrt[15]{ a^{14} }}{a^{2}}\\---------------\)
7. \(\dfrac{a^{-1}}{a^{\frac{-2}{3}}}\\= a^{ -1 - (\frac{-2}{3}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
8. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{1}{3}}}\\= a^{ \frac{1}{2} - \frac{1}{3} }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
9. \(\dfrac{x^{\frac{5}{2}}}{x^{1}}\\= x^{ \frac{5}{2} - 1 }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
10. \(\dfrac{a^{\frac{5}{6}}}{a^{\frac{1}{2}}}\\= a^{ \frac{5}{6} - \frac{1}{2} }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
11. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{2}{5}}}\\= x^{ \frac{3}{5} - \frac{2}{5} }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)
12. \(\dfrac{x^{-1}}{x^{\frac{2}{3}}}\\= x^{ -1 - \frac{2}{3} }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)