Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{5}{2} - (\frac{-1}{2}) }= y^{3}\\\\---------------\)
2. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-1}{4}}}\\= a^{ \frac{-1}{2} - (\frac{-1}{4}) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
3. \(\dfrac{y^{\frac{1}{2}}}{y^{-1}}\\= y^{ \frac{1}{2} - (-1) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
4. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{5}{6}}}\\= y^{ \frac{-5}{2} - \frac{5}{6} }= y^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ y^{10} }}\\=\frac{1}{y^{3}.\sqrt[3]{ y }}=\frac{1}{y^{3}.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{4}}\\---------------\)
5. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{5}{6}}}\\= q^{ \frac{-3}{5} - \frac{5}{6} }= q^{\frac{-43}{30}}\\=\frac{1}{\sqrt[30]{ q^{43} }}\\=\frac{1}{|q|.\sqrt[30]{ q^{13} }}=\frac{1}{|q|.\sqrt[30]{ q^{13} }} \color{purple}{\frac{\sqrt[30]{ q^{17} }}{\sqrt[30]{ q^{17} }}} \\=\frac{\sqrt[30]{ q^{17} }}{|q^{2}|}\\---------------\)
6. \(\dfrac{x^{2}}{x^{2}}\\= x^{ 2 - 2 }= x^{0}\\=1\\---------------\)
7. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{2}{3} - (\frac{-1}{2}) }= x^{\frac{7}{6}}\\=\sqrt[6]{ x^{7} }=|x|.\sqrt[6]{ x }\\---------------\)
8. \(\dfrac{y^{-1}}{y^{\frac{-5}{6}}}\\= y^{ -1 - (\frac{-5}{6}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
9. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{1}{2}}}\\= a^{ \frac{-1}{2} - \frac{1}{2} }= a^{-1}\\=\frac{1}{a}\\---------------\)
10. \(\dfrac{a^{\frac{-4}{5}}}{a^{\frac{4}{3}}}\\= a^{ \frac{-4}{5} - \frac{4}{3} }= a^{\frac{-32}{15}}\\=\frac{1}{\sqrt[15]{ a^{32} }}\\=\frac{1}{a^{2}.\sqrt[15]{ a^{2} }}=\frac{1}{a^{2}.\sqrt[15]{ a^{2} }} \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a^{3}}\\---------------\)
11. \(\dfrac{a^{\frac{-1}{5}}}{a^{-2}}\\= a^{ \frac{-1}{5} - (-2) }= a^{\frac{9}{5}}\\=\sqrt[5]{ a^{9} }=a.\sqrt[5]{ a^{4} }\\---------------\)
12. \(\dfrac{a^{\frac{-1}{4}}}{a^{\frac{-5}{3}}}\\= a^{ \frac{-1}{4} - (\frac{-5}{3}) }= a^{\frac{17}{12}}\\=\sqrt[12]{ a^{17} }=|a|.\sqrt[12]{ a^{5} }\\---------------\)