Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-3}{5}}}\\= q^{ \frac{-1}{2} - (\frac{-3}{5}) }= q^{\frac{1}{10}}\\=\sqrt[10]{ q }\\---------------\)
2. \(\dfrac{x^{\frac{-1}{5}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-1}{5} - \frac{2}{3} }= x^{\frac{-13}{15}}\\=\frac{1}{\sqrt[15]{ x^{13} }}=\frac{1}{\sqrt[15]{ x^{13} }}. \color{purple}{\frac{\sqrt[15]{ x^{2} }}{\sqrt[15]{ x^{2} }}} \\=\frac{\sqrt[15]{ x^{2} }}{x}\\---------------\)
3. \(\dfrac{q^{1}}{q^{1}}\\= q^{ 1 - 1 }= q^{0}\\=1\\---------------\)
4. \(\dfrac{q^{-1}}{q^{\frac{5}{6}}}\\= q^{ -1 - \frac{5}{6} }= q^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ q^{11} }}\\=\frac{1}{|q|.\sqrt[6]{ q^{5} }}=\frac{1}{|q|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{2}|}\\---------------\)
5. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-1}{4}}}\\= y^{ \frac{1}{2} - (\frac{-1}{4}) }= y^{\frac{3}{4}}\\=\sqrt[4]{ y^{3} }\\---------------\)
6. \(\dfrac{x^{1}}{x^{\frac{3}{5}}}\\= x^{ 1 - \frac{3}{5} }= x^{\frac{2}{5}}\\=\sqrt[5]{ x^{2} }\\---------------\)
7. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{5}{2}}}\\= a^{ \frac{2}{5} - \frac{5}{2} }= a^{\frac{-21}{10}}\\=\frac{1}{\sqrt[10]{ a^{21} }}\\=\frac{1}{|a^{2}|.\sqrt[10]{ a }}=\frac{1}{|a^{2}|.\sqrt[10]{ a }} \color{purple}{\frac{\sqrt[10]{ a^{9} }}{\sqrt[10]{ a^{9} }}} \\=\frac{\sqrt[10]{ a^{9} }}{|a^{3}|}\\---------------\)
8. \(\dfrac{q^{2}}{q^{\frac{5}{4}}}\\= q^{ 2 - \frac{5}{4} }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
9. \(\dfrac{a^{\frac{3}{2}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{3}{2} - (\frac{-4}{5}) }= a^{\frac{23}{10}}\\=\sqrt[10]{ a^{23} }=|a^{2}|.\sqrt[10]{ a^{3} }\\---------------\)
10. \(\dfrac{x^{-1}}{x^{-1}}\\= x^{ -1 - (-1) }= x^{0}\\=1\\---------------\)
11. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{3}{4}}}\\= x^{ \frac{1}{2} - \frac{3}{4} }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
12. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{1}{4}}}\\= x^{ \frac{-5}{3} - \frac{1}{4} }= x^{\frac{-23}{12}}\\=\frac{1}{\sqrt[12]{ x^{23} }}\\=\frac{1}{|x|.\sqrt[12]{ x^{11} }}=\frac{1}{|x|.\sqrt[12]{ x^{11} }} \color{purple}{\frac{\sqrt[12]{ x }}{\sqrt[12]{ x }}} \\=\frac{\sqrt[12]{ x }}{|x^{2}|}\\---------------\)