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

Verified step by step guidance

1. Identify the base and the exponents in the expression $(3^3{)}^2$.
2. Recognize that this is a power of a power situation, which can be simplified using the rule $(a^m{)}^n=a^{m\cdot n}$.
3. Apply the power of a power rule: $(3^3{)}^2=3^{3\cdot 2}$.
4. Calculate the new exponent by multiplying the exponents: $3\cdot 2$.
5. Rewrite the expression with the new exponent: $3^6$.

Key Concepts

Exponential Notation

Exponential notation is a mathematical shorthand used to represent repeated multiplication of a number by itself. In the expression a^n, 'a' is the base and 'n' is the exponent, indicating how many times 'a' is multiplied by itself. Understanding this notation is crucial for evaluating expressions involving powers.

Power of a Power Rule

The power of a power rule states that when raising an exponent to another exponent, you multiply the exponents. Mathematically, this is expressed as (a^m)^n = a^(m*n). This rule simplifies the evaluation of expressions like (3^3)^2 by allowing you to combine the exponents directly.

Order of Operations

The order of operations is a set of rules that dictates the sequence in which mathematical operations should be performed to ensure consistent results. The common acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. Applying these rules correctly is essential when evaluating complex expressions.