Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{3}{4}}}\\= y^{ \frac{1}{3} - \frac{3}{4} }= y^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ y^{5} }}=\frac{1}{\sqrt[12]{ y^{5} }}. \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y|}\\---------------\)
2. \(\dfrac{x^{\frac{1}{6}}}{x^{\frac{-1}{5}}}\\= x^{ \frac{1}{6} - (\frac{-1}{5}) }= x^{\frac{11}{30}}\\=\sqrt[30]{ x^{11} }\\---------------\)
3. \(\dfrac{x^{1}}{x^{-1}}\\= x^{ 1 - (-1) }= x^{2}\\\\---------------\)
4. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{3}{5}}}\\= y^{ \frac{-4}{3} - \frac{3}{5} }= y^{\frac{-29}{15}}\\=\frac{1}{\sqrt[15]{ y^{29} }}\\=\frac{1}{y.\sqrt[15]{ y^{14} }}=\frac{1}{y.\sqrt[15]{ y^{14} }} \color{purple}{\frac{\sqrt[15]{ y }}{\sqrt[15]{ y }}} \\=\frac{\sqrt[15]{ y }}{y^{2}}\\---------------\)
5. \(\dfrac{a^{\frac{1}{2}}}{a^{1}}\\= a^{ \frac{1}{2} - 1 }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
6. \(\dfrac{a^{2}}{a^{\frac{1}{3}}}\\= a^{ 2 - \frac{1}{3} }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
7. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{-4}{3}}}\\= y^{ \frac{4}{3} - (\frac{-4}{3}) }= y^{\frac{8}{3}}\\=\sqrt[3]{ y^{8} }=y^{2}.\sqrt[3]{ y^{2} }\\---------------\)
8. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{-5}{3}}}\\= y^{ \frac{-1}{5} - (\frac{-5}{3}) }= y^{\frac{22}{15}}\\=\sqrt[15]{ y^{22} }=y.\sqrt[15]{ y^{7} }\\---------------\)
9. \(\dfrac{y^{\frac{1}{5}}}{y^{\frac{3}{5}}}\\= y^{ \frac{1}{5} - \frac{3}{5} }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)
10. \(\dfrac{y^{-1}}{y^{1}}\\= y^{ -1 - 1 }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
11. \(\dfrac{q^{\frac{-1}{4}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-1}{4} - (\frac{-1}{3}) }= q^{\frac{1}{12}}\\=\sqrt[12]{ q }\\---------------\)
12. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{-1}{2} - (\frac{-1}{2}) }= a^{0}\\=1\\---------------\)