Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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