Evaluate each exponential expression: (-3)^3 (-2)^2

Verified step by step guidance

1. Identify the base and the exponent for each part of the expression: $(-3{)}^3$ and $(-2{)}^2$.
2. Calculate $(-3{)}^3$ by multiplying $-3$ by itself three times: $(-3)\times (-3)\times (-3)$.
3. Calculate $(-2{)}^2$ by multiplying $-2$ by itself two times: $(-2)\times (-2)$.
4. Multiply the results of $(-3{)}^3$ and $(-2{)}^2$ together.
5. Combine the results to find the value of the entire expression.

Key Concepts

Exponential Expressions

Exponential expressions involve a base raised to a power, indicating how many times the base is multiplied by itself. For example, in the expression a^n, 'a' is the base and 'n' is the exponent. Understanding how to evaluate these expressions is crucial for solving problems involving powers.

Negative Bases

When evaluating exponential expressions with negative bases, the sign of the result depends on whether the exponent is odd or even. An odd exponent will yield a negative result, while an even exponent will yield a positive result. For instance, (-3)^3 results in -27, while (-2)^2 results in 4.

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 acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. In evaluating expressions, it's essential to apply these rules correctly to arrive at the right answer.