Problem 6 Evaluate. $$(-12)^{0}$$... [FREE SOLUTION]

Chapter 2: Problem 6

Evaluate. $$(-12)^{0}$$

Short Answer

Expert verified

The short answer to the question 'Evaluate $(-12)^{0}$' is that any non-zero number raised to the power of 0 is equal to 1. Therefore, $(-12)^{0} = 1$.

Step by step solution

Apply the exponent rule for a number raised to the power of 0

We know that any non-zero number raised to the power of 0 is equal to 1. So, let's apply this rule to the given expression: $(-12)^{0} = 1$. There is only one step in solving this particular exercise since the rule is straightforward. The answer to the given exercise is 1.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Zero Exponent Rule

The zero exponent rule is a handy tool in algebra. It states that any non-zero number raised to the power of zero equals one. This might seem a bit strange at first, but there's a simple explanation behind it.

Think of exponents as repeated multiplication. For instance,

$a^3 = a \times a \times a$
$a^2 = a \times a$
$a^1 = a$

Notice that each time the exponent decreases, you're essentially dividing by $a$. Now, if you divide $a$ by itself one more time, you get $a^0 = 1$.

Just remember, the rule doesn鈥檛 apply to zero itself. While $(-12)^0 = 1$, $0^0$ is considered undefined in most contexts.

Algebraic Expressions

Algebraic expressions are combinations of numbers, variables, and operations. They are the building blocks of algebra and can represent various situations and problems.

Consider expressions like $x + 2$ or $3y^2 - 4y + 5$. These allow us to model real-world scenarios by using variables to stand in for unknown quantities.

Understanding how to manipulate and simplify these expressions using rules, like the zero exponent rule, is essential.

Key components include:

Variables: letters representing unknowns or changing quantities
Coefficients: numbers multiplying variables
Constants: specific numbers

These components can be combined in more complex ways to solve a range of problems.

Evaluating Expressions

Evaluating expressions means finding their value given certain conditions or values for the variables involved. It often involves substituting numbers for variables and simplifying the resulting expression.

For example, consider the expression $3x^2 - 2x + 1$. To find its value when $x = 2$, substitute 2 in for $x$:

$3(2)^2 - 2(2) + 1 = 3 \times 4 - 4 + 1 = 12 - 4 + 1 = 9$

When evaluating, use skills like the order of operations and exponent rules to ensure accuracy. The zero exponent rule simplifies expressions drastically by reducing elements raised to the zero power to 1, as seen in examples like $(-12)^0$.

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91影视

Evaluate. $$(-12)^{0}$$

Short Answer

Step by step solution

Apply the exponent rule for a number raised to the power of 0

Key Concepts

Zero Exponent Rule

Algebraic Expressions

Evaluating Expressions

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