directions: Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s

Question

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 \(\frac{1}{46656}\).