Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{-5}{3}}}\\= a^{ \frac{3}{5} - (\frac{-5}{3}) }= a^{\frac{34}{15}}\\=\sqrt[15]{ a^{34} }=a^{2}.\sqrt[15]{ a^{4} }\\---------------\)
2. \(\dfrac{a^{1}}{a^{\frac{-3}{4}}}\\= a^{ 1 - (\frac{-3}{4}) }= a^{\frac{7}{4}}\\=\sqrt[4]{ a^{7} }=|a|.\sqrt[4]{ a^{3} }\\---------------\)
3. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-1}{3} - \frac{1}{3} }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
4. \(\dfrac{y^{1}}{y^{-1}}\\= y^{ 1 - (-1) }= y^{2}\\\\---------------\)
5. \(\dfrac{x^{\frac{-2}{3}}}{x^{-1}}\\= x^{ \frac{-2}{3} - (-1) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
6. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{-1}{5}}}\\= y^{ \frac{-2}{3} - (\frac{-1}{5}) }= y^{\frac{-7}{15}}\\=\frac{1}{\sqrt[15]{ y^{7} }}=\frac{1}{\sqrt[15]{ y^{7} }}. \color{purple}{\frac{\sqrt[15]{ y^{8} }}{\sqrt[15]{ y^{8} }}} \\=\frac{\sqrt[15]{ y^{8} }}{y}\\---------------\)
7. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-1}{2} - \frac{1}{3} }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
8. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{1}{5}}}\\= y^{ \frac{-1}{3} - \frac{1}{5} }= y^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ y^{8} }}=\frac{1}{\sqrt[15]{ y^{8} }}. \color{purple}{\frac{\sqrt[15]{ y^{7} }}{\sqrt[15]{ y^{7} }}} \\=\frac{\sqrt[15]{ y^{7} }}{y}\\---------------\)
9. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{1}{2} - (\frac{-2}{3}) }= a^{\frac{7}{6}}\\=\sqrt[6]{ a^{7} }=|a|.\sqrt[6]{ a }\\---------------\)
10. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{-1}{5}}}\\= x^{ \frac{-2}{5} - (\frac{-1}{5}) }= x^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ x }}=\frac{1}{\sqrt[5]{ x }}. \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x}\\---------------\)
11. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-3}{4}}}\\= q^{ \frac{-1}{2} - (\frac{-3}{4}) }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
12. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{3}{2}}}\\= y^{ \frac{2}{5} - \frac{3}{2} }= y^{\frac{-11}{10}}\\=\frac{1}{\sqrt[10]{ y^{11} }}\\=\frac{1}{|y|.\sqrt[10]{ y }}=\frac{1}{|y|.\sqrt[10]{ y }} \color{purple}{\frac{\sqrt[10]{ y^{9} }}{\sqrt[10]{ y^{9} }}} \\=\frac{\sqrt[10]{ y^{9} }}{|y^{2}|}\\---------------\)