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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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