\(4\left(3x^3+1^{10}\right)=4\cdot5^2\)
=>\(4\left(3x^3+1\right)=4\cdot25=100\)
=>\(3x^3+1=25\)
=>\(3x^3=24\)
=>\(x^3=8\)
=>\(x=\sqrt[3]{8}=2\)
\(4\cdot\left(3x^3+1^{10}\right)=4\cdot5^2\)
\(\Rightarrow3x^3+1=\dfrac{4\cdot5^2}{4}\)
\(\Rightarrow3x^3+1=5^2\)
\(\Rightarrow3x^3=25-1\)
\(\Rightarrow3x^3=24\)
\(\Rightarrow x^3=\dfrac{24}{3}\)
\(\Rightarrow x^3=8\)
\(\Rightarrow x^3=2^3\)
\(\Rightarrow x=2\)