Problem 16 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

The evaluated value of the exponential expression \((3^{3})^{2}\) is 729.

Step 1: Base and Exponent

Identify the base and the exponents. Here, the base is 3, and there are two exponents: 3 and 2.

Step 2: Apply Rule of Exponents

According to the rules of exponents, \((a^{m})^{n}\) is equal to \(a^{m*n}\). Apply this rule to \(3^{3^{2}}\). The calculation becomes \(3^{3*2}\).

Step 3: Simplify Expression

Evaulate \(3^{3*2}\) to simplify the expression. This results in \(3^{6}\).

Step 4: Evaluate Exponential Expression

Finally, compute the value of \(3^{6}\) which equals to 729.