Question

(4^x)^2=16.2^(x^2). O valor do X elevado a X é ?

Answer 1

$(4^{x})^2=16\cdot2^{x^2}$

$4^{2x}=16\cdot2^{x^2}$

$(2^2)^{2x}=2^4\cdot2^{x^2}$

$2^{4x}=2^{x^2+4}$

$x^2+4=4x$

$x^2-4x+4=0$

$\Delta=(-4)^2-4\cdot1\cdot4=16-16=0$

$x=\dfrac{-(-4)\pm\sqrt{0}}{2}=\dfrac{4}{2}=2$

$x^{x}=2^2=4$