To simplify the given expression [tex]\(\left(b^5\right)^4\)[/tex], we apply the power rule for exponents. This rule states that when raising an exponentiated term to another power, you multiply the exponents. The power rule can be written as [tex]\((a^m)^n = a^{m \cdot n}\)[/tex].
Let's simplify the expression step-by-step:
1. Identify the base and the exponents. In this case, the base is [tex]\(b\)[/tex], the first exponent is [tex]\(5\)[/tex], and the second exponent is [tex]\(4\)[/tex].
2. According to the power rule, we multiply the exponents [tex]\(5\)[/tex] and [tex]\(4\)[/tex].
Thus, we get:
[tex]\[
(b^5)^4 = b^{5 \cdot 4}
\][/tex]
3. Now calculate the product of the exponents:
[tex]\[
5 \cdot 4 = 20
\][/tex]
4. Substituting the result back into the expression, we have:
[tex]\[
(b^5)^4 = b^{20}
\][/tex]
Therefore, the correct simplification of the expression [tex]\(\left(b^5\right)^4\)[/tex] is [tex]\(b^{20}\)[/tex].
So, the correct answer is:
[tex]\[
b^{20}
\][/tex]
