Questions: Evaluate. Write your answer as a whole number 8^9 * 8^-2 * 8^-6 =

Evaluate. Write your answer as a whole number 8^9 * 8^-2 * 8^-6 =
Transcript text: Evaluate. Write your answer as a whole number \[ 8^{9} \cdot 8^{-2} \cdot 8^{-6}= \]
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Solution

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Solution Steps

To evaluate the expression \(8^{9} \cdot 8^{-2} \cdot 8^{-6}\), we can use the exponent rules. Specifically, when multiplying powers with the same base, we add the exponents. Therefore, we add the exponents 9, -2, and -6 together and then compute the power of 8 with the resulting exponent.

Step 1: Apply Exponent Rules

To evaluate the expression \(8^{9} \cdot 8^{-2} \cdot 8^{-6}\), we use the rule for multiplying powers with the same base: add the exponents. Therefore, we calculate the sum of the exponents:

\[ 9 + (-2) + (-6) = 1 \]

Step 2: Calculate the Power

With the combined exponent, the expression simplifies to:

\[ 8^{1} = 8 \]

Final Answer

The value of the expression is \(\boxed{8}\).

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