Werk uit m.b.v. de rekenregels
- \(\left(x^{\frac{5}{4}}\right)^{\frac{2}{3}}\)
- \(\left(q^{1}\right)^{1}\)
- \(\left(x^{\frac{1}{3}}\right)^{2}\)
- \(\left(x^{\frac{2}{3}}\right)^{\frac{1}{6}}\)
- \(\left(a^{\frac{5}{3}}\right)^{\frac{5}{4}}\)
- \(\left(q^{-1}\right)^{\frac{-5}{6}}\)
- \(\left(a^{1}\right)^{\frac{1}{2}}\)
- \(\left(a^{\frac{-3}{4}}\right)^{-1}\)
- \(\left(x^{\frac{1}{6}}\right)^{\frac{-3}{2}}\)
- \(\left(x^{\frac{3}{2}}\right)^{-1}\)
- \(\left(y^{-1}\right)^{\frac{5}{4}}\)
- \(\left(y^{\frac{3}{4}}\right)^{\frac{-1}{3}}\)
Werk uit m.b.v. de rekenregels
Verbetersleutel
- \(\left(x^{\frac{5}{4}}\right)^{\frac{2}{3}}\\= x^{ \frac{5}{4} . \frac{2}{3} }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
- \(\left(q^{1}\right)^{1}\\= q^{ 1 . 1 }= q^{1}\\\\---------------\)
- \(\left(x^{\frac{1}{3}}\right)^{2}\\= x^{ \frac{1}{3} . 2 }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
- \(\left(x^{\frac{2}{3}}\right)^{\frac{1}{6}}\\= x^{ \frac{2}{3} . \frac{1}{6} }= x^{\frac{1}{9}}\\=\sqrt[9]{ x }\\---------------\)
- \(\left(a^{\frac{5}{3}}\right)^{\frac{5}{4}}\\= a^{ \frac{5}{3} . \frac{5}{4} }= a^{\frac{25}{12}}\\=\sqrt[12]{ a^{25} }=|a^{2}|.\sqrt[12]{ a }\\---------------\)
- \(\left(q^{-1}\right)^{\frac{-5}{6}}\\= q^{ -1 . (\frac{-5}{6}) }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
- \(\left(a^{1}\right)^{\frac{1}{2}}\\= a^{ 1 . \frac{1}{2} }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
- \(\left(a^{\frac{-3}{4}}\right)^{-1}\\= a^{ \frac{-3}{4} . (-1) }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
- \(\left(x^{\frac{1}{6}}\right)^{\frac{-3}{2}}\\= x^{ \frac{1}{6} . (\frac{-3}{2}) }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}.
\color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
- \(\left(x^{\frac{3}{2}}\right)^{-1}\\= x^{ \frac{3}{2} . (-1) }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } }
\color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
- \(\left(y^{-1}\right)^{\frac{5}{4}}\\= y^{ -1 . \frac{5}{4} }= y^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ y^{5} }}\\=\frac{1}{|y|.\sqrt[4]{ y }}=\frac{1}{|y|.\sqrt[4]{ y }}
\color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{2}|}\\---------------\)
- \(\left(y^{\frac{3}{4}}\right)^{\frac{-1}{3}}\\= y^{ \frac{3}{4} . (\frac{-1}{3}) }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}.
\color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)