Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{1}{2}}}{y^{1}}\\= y^{ \frac{1}{2} - 1 }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
2. \(\dfrac{x^{\frac{-3}{4}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{-3}{4} - (\frac{-3}{4}) }= x^{0}\\=1\\---------------\)
3. \(\dfrac{x^{\frac{-5}{6}}}{x^{1}}\\= x^{ \frac{-5}{6} - 1 }= x^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ x^{11} }}\\=\frac{1}{|x|.\sqrt[6]{ x^{5} }}=\frac{1}{|x|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{2}|}\\---------------\)
4. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{-1}{3} - (\frac{-3}{5}) }= y^{\frac{4}{15}}\\=\sqrt[15]{ y^{4} }\\---------------\)
5. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{-4}{5} - (\frac{-3}{5}) }= x^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ x }}=\frac{1}{\sqrt[5]{ x }}. \color{purple}{\frac{\sqrt[5]{ x^{4} }}{\sqrt[5]{ x^{4} }}} \\=\frac{\sqrt[5]{ x^{4} }}{x}\\---------------\)
6. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{-4}{3} - (\frac{-5}{2}) }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)
7. \(\dfrac{x^{\frac{-3}{4}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{-3}{4} - (\frac{-5}{4}) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
8. \(\dfrac{a^{\frac{-5}{4}}}{a^{-2}}\\= a^{ \frac{-5}{4} - (-2) }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
9. \(\dfrac{a^{\frac{-5}{3}}}{a^{1}}\\= a^{ \frac{-5}{3} - 1 }= a^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ a^{8} }}\\=\frac{1}{a^{2}.\sqrt[3]{ a^{2} }}=\frac{1}{a^{2}.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{3}}\\---------------\)
10. \(\dfrac{q^{\frac{-4}{3}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{-4}{3} - (\frac{-1}{5}) }= q^{\frac{-17}{15}}\\=\frac{1}{\sqrt[15]{ q^{17} }}\\=\frac{1}{q.\sqrt[15]{ q^{2} }}=\frac{1}{q.\sqrt[15]{ q^{2} }} \color{purple}{\frac{\sqrt[15]{ q^{13} }}{\sqrt[15]{ q^{13} }}} \\=\frac{\sqrt[15]{ q^{13} }}{q^{2}}\\---------------\)
11. \(\dfrac{q^{\frac{-4}{5}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{-4}{5} - (\frac{-1}{5}) }= q^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ q^{3} }}=\frac{1}{\sqrt[5]{ q^{3} }}. \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q}\\---------------\)
12. \(\dfrac{q^{-1}}{q^{\frac{4}{5}}}\\= q^{ -1 - \frac{4}{5} }= q^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ q^{9} }}\\=\frac{1}{q.\sqrt[5]{ q^{4} }}=\frac{1}{q.\sqrt[5]{ q^{4} }} \color{purple}{\frac{\sqrt[5]{ q }}{\sqrt[5]{ q }}} \\=\frac{\sqrt[5]{ q }}{q^{2}}\\---------------\)