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Chapter 0: Problem 19

Evaluate each exponential expression. $$3^{-3} \cdot 3$$

Short Answer

Expert verified
The given exponential expression, \(3^{-3} \cdot 3\), simplifies to \(1 / 9\).

Step by step solution

01

Calculating the Exponential

Given the expression \(3^{-3} \cdot 3\), the exponent -3 signifies the reciprocal of the base. Hence, \(3^{-3}\) evaluates to \(1 / 3^{3}\). Calculate the value of \(3^{3}\) which is 27. Therefore, \(3^{-3}\) evaluates to \(1 / 27\).
02

Multiplying the Results

Now we have \(1 / 27 \cdot 3\), which simplifies to \(3 / 27\).
03

Simplifying the Expression

Finally, simplify \(3 / 27\) to its lowest terms, which is \(1 / 9\). This is done by dividing both numerator and denominator by their greatest common divisor, which in this case is 3.

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