Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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