Question

Use the Power Rule of Exponents to simplify the expression (86)4

Show your work.

(1 point)
Responses

810
8 to the 10th power

824
8 to the 24th power

82
8 squared

564

Answer 1

To simplify the expression \((86)^4\) using the Power Rule of Exponents, we follow these steps:

1. **Identify the base and exponent**: The base here is 86 and the exponent is 4.
2. **Apply the Power Rule of Exponents**: The Power Rule states that \((a^m)^n = a^{m \cdot n}\). In this case, we can rewrite the base 86 as \(8^n\) where n is to be determined.

So, we first express \(86\) in terms of its prime factorization. \(86\) can be factored into \(2 \times 43\). However, this does not apply here since we only need to calculate the power.

Next, we can simplify \((86)^4\) as follows:

\[
(86)^4 = (8 \cdot 10.75)^4
\]

This doesn't help us much either, so let’s focus back on directly simplifying:

Since 86 does not directly relate to \(8^n\) where \(n \in \mathbb{Z}, n>0\), let's raise in power:

After evaluating \(86^4\) carefully:

\[
= (8^{1})^{4} \implies 8^{4 \times n} = 8^{4}
\]

Which leads us to \(8^{24}\).

Hence, the simplified version of \( (86)^4 \) is:

\[
\text{None of the options given.}
\]

However, if re-evaluating from original:

Let’s see if sticking large with Powers make sense:

Re-evaluating with \(8^4 = 4096\)

Hereby:

Assuming output would

- None of the provided responses are correct based on calculation for simplification purely.