Problem 16

Question

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

Step-by-Step Solution

Verified
Answer
The value of the given exponential expression is 729.
1Step 1: 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 \(3^{6}\).
2Step 2: 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.