Evaluate each expression. (-2)^4

Verified step by step guidance

1. Identify the base and the exponent in the expression $(-2{)}^4$. Here, the base is $-2$ and the exponent is $4$.
2. Understand that the exponent $4$ indicates that the base $-2$ should be multiplied by itself a total of four times.
3. Write the expression as a repeated multiplication: $(-2)\times (-2)\times (-2)\times (-2)$.
4. Calculate the product of the first two terms: $(-2)\times (-2)=4$.
5. Continue multiplying the result by the next $-2$ until all terms are used: $4\times (-2)=-8$ and then $-8\times (-2)$.

Key Concepts

Exponentiation

Exponentiation is a mathematical operation involving two numbers, the base and the exponent. The exponent indicates 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 this concept is crucial for evaluating expressions like (-2)^4.

Negative Numbers

Negative numbers are values less than zero, represented with a minus sign. When raised to an even exponent, negative numbers yield a positive result, as the negative signs cancel each other out. This property is essential for evaluating expressions involving negative bases, such as (-2)^4, where the outcome will be positive.

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. In evaluating (-2)^4, recognizing that exponentiation is performed before multiplication or addition is key to arriving at the correct answer.