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Chapter 0: Problem 16

Evaluate each exponential expression. $$ \left(3^{3}\right)^{2} $$

Short Answer

Expert verified
The value of the given exponential expression is 729.

Step by step solution

01

Break Down the Exponential Expression

For any numbers \(x\) and \(y\), \((x^{y})^{z} = x^{y \cdot z}\). So, applying this rule, the expression \((3^{3})^{2}\) is equivalent to \(3^{3 \cdot 2}\), which simplifies to \(3^{6}\).
02

Calculate the Value of the Exponential Expression

Next, calculate the value of \(3^{6}\). This involves multiplying \(3\) by itself five more times. The outcome is 729.

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