[tex]\bf \left( x^{4a-3} \right)^2=x^{10}\implies x^{(4a-3)2}=x^{10}
\\\\\\
\textit{since the bases are the same, the exponents must also be the same}
\\\\\\
2(4a-3)=10\implies 4a-3=\cfrac{10}{2}\implies 4a-3=5\implies 4a=8
\\\\\\
a=\cfrac{8}{4}\implies \boxed{a=2}[/tex]
