Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-2}{3} - (\frac{-1}{2}) }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
2. \(\dfrac{q^{\frac{-1}{3}}}{q^{-2}}\\= q^{ \frac{-1}{3} - (-2) }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
3. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-3}{4} - (\frac{-1}{2}) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
4. \(\dfrac{y^{\frac{-1}{4}}}{y^{\frac{1}{5}}}\\= y^{ \frac{-1}{4} - \frac{1}{5} }= y^{\frac{-9}{20}}\\=\frac{1}{\sqrt[20]{ y^{9} }}=\frac{1}{\sqrt[20]{ y^{9} }}. \color{purple}{\frac{\sqrt[20]{ y^{11} }}{\sqrt[20]{ y^{11} }}} \\=\frac{\sqrt[20]{ y^{11} }}{|y|}\\---------------\)
5. \(\dfrac{y^{-1}}{y^{-1}}\\= y^{ -1 - (-1) }= y^{0}\\=1\\---------------\)
6. \(\dfrac{a^{\frac{-1}{5}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-1}{5} - (\frac{-1}{3}) }= a^{\frac{2}{15}}\\=\sqrt[15]{ a^{2} }\\---------------\)
7. \(\dfrac{a^{\frac{4}{5}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{4}{5} - (\frac{-3}{5}) }= a^{\frac{7}{5}}\\=\sqrt[5]{ a^{7} }=a.\sqrt[5]{ a^{2} }\\---------------\)
8. \(\dfrac{q^{\frac{5}{3}}}{q^{\frac{3}{2}}}\\= q^{ \frac{5}{3} - \frac{3}{2} }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
9. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{5}{6}}}\\= q^{ \frac{5}{6} - \frac{5}{6} }= q^{0}\\=1\\---------------\)
10. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{4}{5}}}\\= x^{ \frac{-1}{2} - \frac{4}{5} }= x^{\frac{-13}{10}}\\=\frac{1}{\sqrt[10]{ x^{13} }}\\=\frac{1}{|x|.\sqrt[10]{ x^{3} }}=\frac{1}{|x|.\sqrt[10]{ x^{3} }} \color{purple}{\frac{\sqrt[10]{ x^{7} }}{\sqrt[10]{ x^{7} }}} \\=\frac{\sqrt[10]{ x^{7} }}{|x^{2}|}\\---------------\)
11. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-1}{3} - \frac{1}{3} }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
12. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{3}{2}}}\\= y^{ \frac{2}{3} - \frac{3}{2} }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)