Question

directions: Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s
Simplify the following expression, and then find its value.
(6^-4)^2 (6^2) (6^7)^0

The simplified expression is 6 raised to the power of blank

The value of the simplified expression is blank
.

Answer 1

Let's simplify the expression step by step.

The given expression is:
\[
(6^{-4})^2 (6^2) (6^7)^0
\]

First, we simplify each part:

1. **Simplifying \((6^{-4})^2\)**:
\[
(6^{-4})^2 = 6^{-8}
\]

2. **Simplifying \( (6^7)^0 \)**:
Any non-zero number raised to the power of 0 is 1, so:
\[
(6^7)^0 = 1
\]

Now, substitute back into the expression:
\[
6^{-8} \cdot 6^2 \cdot 1
\]

Next, we combine the powers of 6:
\[
6^{-8 + 2} = 6^{-6}
\]

Thus, the simplified expression is:
\[
6^{-6}
\]

### To fill in the answers:
- The simplified expression is \(6\) raised to the power of \(-6\).

Now, to find the value of the simplified expression:
\[
6^{-6} = \frac{1}{6^6}
\]

Calculating \(6^6\):
\[
6^6 = 46656
\]

Thus:
\[
6^{-6} = \frac{1}{46656}
\]

### Final answers:
- The simplified expression is \(6\) raised to the power of \(-6\).
- The value of the simplified expression is \(\frac{1}{46656}\).