Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{5}{3} - (\frac{-4}{3}) }= x^{3}\\\\---------------\)
2. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{-5}{4}}}\\= y^{ \frac{-3}{5} - (\frac{-5}{4}) }= y^{\frac{13}{20}}\\=\sqrt[20]{ y^{13} }\\---------------\)
3. \(\dfrac{y^{\frac{2}{3}}}{y^{-1}}\\= y^{ \frac{2}{3} - (-1) }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
4. \(\dfrac{a^{\frac{1}{4}}}{a^{1}}\\= a^{ \frac{1}{4} - 1 }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
5. \(\dfrac{y^{-1}}{y^{-1}}\\= y^{ -1 - (-1) }= y^{0}\\=1\\---------------\)
6. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{-1}{4}}}\\= a^{ \frac{-5}{3} - (\frac{-1}{4}) }= a^{\frac{-17}{12}}\\=\frac{1}{\sqrt[12]{ a^{17} }}\\=\frac{1}{|a|.\sqrt[12]{ a^{5} }}=\frac{1}{|a|.\sqrt[12]{ a^{5} }} \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a^{2}|}\\---------------\)
7. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{-4}{5} - (\frac{-5}{2}) }= y^{\frac{17}{10}}\\=\sqrt[10]{ y^{17} }=|y|.\sqrt[10]{ y^{7} }\\---------------\)
8. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-5}{3} - \frac{1}{3} }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
9. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-1}{4}}}\\= a^{ \frac{1}{2} - (\frac{-1}{4}) }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
10. \(\dfrac{y^{1}}{y^{\frac{-1}{3}}}\\= y^{ 1 - (\frac{-1}{3}) }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
11. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{3}{4} - (\frac{-1}{2}) }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
12. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{3}{4}}}\\= x^{ \frac{4}{5} - \frac{3}{4} }= x^{\frac{1}{20}}\\=\sqrt[20]{ x }\\---------------\)