Sure, let's solve the given expression step by step.
We have the expression [tex]\(\left(5 x^4\right)^0\)[/tex] within the context of a larger expression [tex]\(2 \left(5 x^4\right)^0\)[/tex].
First, let's recall a fundamental property of exponents: any number or expression raised to the power of 0 equals 1. This is true regardless of the base, as long as the base is not 0. Mathematically, this can be expressed as:
[tex]\[a^0 = 1 \quad \text{for any non-zero } a\][/tex]
So in our given expression [tex]\(\left(5 x^4\right)^0\)[/tex], the entire base [tex]\(5 x^4\)[/tex] is raised to the power of 0. Applying the property of exponents, we get:
[tex]\[
\left(5 x^4\right)^0 = 1
\][/tex]
Now we incorporate this result back into the larger expression:
[tex]\[
2 \left(5 x^4\right)^0 = 2 \times 1
\][/tex]
Finally, multiplying 2 by 1 gives us:
[tex]\[
2 \times 1 = 2
\][/tex]
Thus, the value of the expression [tex]\(2 \left(5 x^4\right)^0\)[/tex] is:
[tex]\[
\boxed{2}
\][/tex]
