Evaluate each exponential expression in Exercises 1–22. $(3^3{)}^2$

Verified step by step guidance

1. Identify the given expression: \( (3^3)^2 \). This is a power raised to another power.
2. Recall the exponent rule for powers raised to powers: \( (a^m)^n = a^{m \times n} \).
3. Apply the rule by multiplying the exponents: \( 3^{3 \times 2} \).
4. Simplify the exponent multiplication: \( 3^6 \).
5. Evaluate \( 3^6 \) by multiplying 3 by itself 6 times (if needed, but the problem only asks to express the simplified form).

Key Concepts

Exponents and Powers

Exponents indicate how many times a base number is multiplied by itself. For example, 3^3 means 3 multiplied by itself three times (3 × 3 × 3). Understanding this helps in evaluating expressions involving powers.

Power of a Power Rule

When an exponent is raised to another exponent, multiply the exponents. For instance, (3^3)^2 equals 3^(3×2) = 3^6. This rule simplifies expressions with nested exponents.

Evaluating Exponential Expressions

After simplifying the exponents, calculate the numerical value by multiplying the base the required number of times. For example, 3^6 = 3 × 3 × 3 × 3 × 3 × 3 = 729.