Werk uit m.b.v. de rekenregels
- \(\left(x^{\frac{1}{5}}\right)^{2}\)
- \(\left(y^{\frac{-4}{5}}\right)^{1}\)
- \(\left(a^{\frac{-2}{3}}\right)^{\frac{1}{2}}\)
- \(\left(a^{\frac{-1}{4}}\right)^{\frac{-3}{4}}\)
- \(\left(x^{\frac{2}{3}}\right)^{\frac{-3}{5}}\)
- \(\left(x^{\frac{2}{5}}\right)^{-1}\)
- \(\left(y^{\frac{-5}{2}}\right)^{\frac{-3}{5}}\)
- \(\left(y^{-1}\right)^{-1}\)
- \(\left(y^{\frac{1}{4}}\right)^{-2}\)
- \(\left(a^{\frac{-5}{4}}\right)^{\frac{5}{4}}\)
- \(\left(x^{\frac{-4}{5}}\right)^{\frac{-1}{5}}\)
- \(\left(q^{\frac{1}{2}}\right)^{\frac{-3}{4}}\)
Werk uit m.b.v. de rekenregels
Verbetersleutel
- \(\left(x^{\frac{1}{5}}\right)^{2}\\= x^{ \frac{1}{5} . 2 }= x^{\frac{2}{5}}\\=\sqrt[5]{ x^{2} }\\---------------\)
- \(\left(y^{\frac{-4}{5}}\right)^{1}\\= y^{ \frac{-4}{5} . 1 }= y^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ y^{4} }}=\frac{1}{\sqrt[5]{ y^{4} }}.
\color{purple}{\frac{\sqrt[5]{ y }}{\sqrt[5]{ y }}} \\=\frac{\sqrt[5]{ y }}{y}\\---------------\)
- \(\left(a^{\frac{-2}{3}}\right)^{\frac{1}{2}}\\= a^{ \frac{-2}{3} . \frac{1}{2} }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}.
\color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
- \(\left(a^{\frac{-1}{4}}\right)^{\frac{-3}{4}}\\= a^{ \frac{-1}{4} . (\frac{-3}{4}) }= a^{\frac{3}{16}}\\=\sqrt[16]{ a^{3} }\\---------------\)
- \(\left(x^{\frac{2}{3}}\right)^{\frac{-3}{5}}\\= x^{ \frac{2}{3} . (\frac{-3}{5}) }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}.
\color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
- \(\left(x^{\frac{2}{5}}\right)^{-1}\\= x^{ \frac{2}{5} . (-1) }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}.
\color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
- \(\left(y^{\frac{-5}{2}}\right)^{\frac{-3}{5}}\\= y^{ \frac{-5}{2} . (\frac{-3}{5}) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
- \(\left(y^{-1}\right)^{-1}\\= y^{ -1 . (-1) }= y^{1}\\\\---------------\)
- \(\left(y^{\frac{1}{4}}\right)^{-2}\\= y^{ \frac{1}{4} . (-2) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }.
\color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
- \(\left(a^{\frac{-5}{4}}\right)^{\frac{5}{4}}\\= a^{ \frac{-5}{4} . \frac{5}{4} }= a^{\frac{-25}{16}}\\=\frac{1}{\sqrt[16]{ a^{25} }}\\=\frac{1}{|a|.\sqrt[16]{ a^{9} }}=\frac{1}{|a|.\sqrt[16]{ a^{9} }}
\color{purple}{\frac{\sqrt[16]{ a^{7} }}{\sqrt[16]{ a^{7} }}} \\=\frac{\sqrt[16]{ a^{7} }}{|a^{2}|}\\---------------\)
- \(\left(x^{\frac{-4}{5}}\right)^{\frac{-1}{5}}\\= x^{ \frac{-4}{5} . (\frac{-1}{5}) }= x^{\frac{4}{25}}\\=\sqrt[25]{ x^{4} }\\---------------\)
- \(\left(q^{\frac{1}{2}}\right)^{\frac{-3}{4}}\\= q^{ \frac{1}{2} . (\frac{-3}{4}) }= q^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ q^{3} }}=\frac{1}{\sqrt[8]{ q^{3} }}.
\color{purple}{\frac{\sqrt[8]{ q^{5} }}{\sqrt[8]{ q^{5} }}} \\=\frac{\sqrt[8]{ q^{5} }}{|q|}\\---------------\)