Bentuk sederhana operasi perpangkatan:
[tex]\begin{aligned}&{\sf{a.~\left(2^{\frac{2}{5}}\right)^{\frac{5}{4}}=\boldsymbol{\sqrt{\textsf{\textbf{2}}}}}}\\&{\sf{b.~\left(\sqrt[\sf3]{\sf6^{\frac{2}{5}}}\right)^{30}=\textsf{\textbf{6}}^{\textsf{\textbf{4}}}}}\end{aligned}[/tex]
Pembahasan
–› Bagian a
[tex]\begin{aligned}{\sf{\left(2^{\frac{2}{5}}\right)^{\frac{5}{4}}}}&={\sf{2^{\frac{2}{5}\times\frac{5}{4}}}}\\&={\sf{2^{\frac{10}{20}}}}\\&={\sf{2^{\frac{1}{2}}}}\\&=\sqrt{\sf{2}}\\\end{aligned}[/tex]
–› Bagian b
[tex]\begin{aligned}{\sf{\left(\sqrt[\sf3]{6^{\frac{2}{5}}}\right)^{30}}}&={\sf{\left(6^{\frac{2}{5}\times\frac{1}{3}}\right)^{30}}}\\&={\sf{\left(6^{\frac{2}{15}}\right)^{30}}}\\&={\sf{6^{\frac{2}{15}\times30}}}\\&={\sf{6^{\frac{60}{15}}}}\\&={\sf{6^4}}\end{aligned}[/tex]
[answer.2.content]
