To simplify the expression [tex]\((8.1)\left(8.1^2\right)^4\)[/tex], we can follow these steps:
1. Understand the expression:
[tex]\[
(8.1) \left(8.1^2\right)^4
\][/tex]
2. Simplify the exponent part:
The expression inside the parentheses is [tex]\((8.1^2)^4\)[/tex]. According to the laws of exponents, [tex]\((a^m)^n = a^{m \cdot n}\)[/tex]. So:
[tex]\[
(8.1^2)^4 = 8.1^{2 \cdot 4}
\][/tex]
3. Multiply the exponents:
[tex]\[
2 \cdot 4 = 8
\][/tex]
Thus, [tex]\((8.1^2)^4\)[/tex] simplifies to [tex]\(8.1^8\)[/tex].
4. Substitute back into the original expression:
We now have:
[tex]\[
(8.1) \left(8.1^8\right)
\][/tex]
5. Combine the bases:
Since the bases are the same, we add the exponents:
[tex]\[
8.1^{1} \cdot 8.1^8 = 8.1^{1 + 8}
\][/tex]
6. Add the exponents:
[tex]\[
1 + 8 = 9
\][/tex]
So, the expression simplifies to:
[tex]\[
(8.1)^9
\][/tex]
Thus, the simplified expression is [tex]\((8.1)^9\)[/tex].
