Questions: For the exponential function f(x)=4 * 6^x, what is the value of f(-3)?

For the exponential function f(x)=4 * 6^x, what is the value of f(-3)?
Transcript text: For the exponential function $f(x)=4 \cdot 6^{x}$, what is the value of $f(-3)$ ?
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Solution

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Solution Steps

Step 1: Substitute \( x = -3 \) into the function

Substitute \( x = -3 \) into the exponential function \( f(x) = 4 \cdot 6^{x} \): \[ f(-3) = 4 \cdot 6^{-3} \]

Step 2: Simplify the exponent

Simplify \( 6^{-3} \) using the property of exponents \( a^{-n} = \frac{1}{a^{n}} \): \[ 6^{-3} = \frac{1}{6^{3}} = \frac{1}{216} \]

Step 3: Multiply by the coefficient

Multiply \( 4 \) by \( \frac{1}{216} \): \[ f(-3) = 4 \cdot \frac{1}{216} = \frac{4}{216} = \frac{1}{54} \]

Final Answer

\(\boxed{\frac{1}{54}}\)

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