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\left(\frac{1}{5}+2x^{3}\right)^{2}
Multiply \frac{1}{5}+2x^{3} and \frac{1}{5}+2x^{3} to get \left(\frac{1}{5}+2x^{3}\right)^{2}.
\frac{1}{25}+\frac{4}{5}x^{3}+4\left(x^{3}\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\frac{1}{5}+2x^{3}\right)^{2}.
\frac{1}{25}+\frac{4}{5}x^{3}+4x^{6}
To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.
\left(\frac{1}{5}+2x^{3}\right)^{2}
Multiply \frac{1}{5}+2x^{3} and \frac{1}{5}+2x^{3} to get \left(\frac{1}{5}+2x^{3}\right)^{2}.
\frac{1}{25}+\frac{4}{5}x^{3}+4\left(x^{3}\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\frac{1}{5}+2x^{3}\right)^{2}.
\frac{1}{25}+\frac{4}{5}x^{3}+4x^{6}
To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.