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Chapter 4: Problem 6

Decide whether each expression is equal to \(0,1,\) or \(-1 .\) $$ -6^{0} $$

Short Answer

Expert verified
The expression is equal to -1.

Step by step solution

01

Understand the Zero Exponent Rule

According to the Zero Exponent Rule, any non-zero number raised to the power of zero is equal to 1. Hence, for any number 'a', we have: a^0 = 1This rule will help evaluate the given expression.
02

Apply the Zero Exponent Rule

The given expression is -6^0 .First identify the base and the exponent. Here, the base is 6, and the exponent is 0.
03

Evaluate the Exponent

Apply the Zero Exponent Rule to the base 6. Since any number raised to the power of 0 is 1, we have:6^0 = 1
04

Apply the Negative Sign

Now consider the negative sign before the base. The negative sign remains unaffected by the exponent because it is separate. Thus, we get:-(6^0) = -1

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Key Concepts

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

headline of the respective core concept
Understanding exponents is crucial in many areas of math, especially algebra. An exponent is a number that indicates how many times to multiply the base number by itself.
For example, in the expression \(2^3\), the base is 2 and the exponent is 3, meaning you multiply 2 by itself three times (\(2 \times 2 \times 2 = 8\)).
These rules apply to simple numbers and also extend to more complex algebraic terms.
Knowing exponent rules, like the Zero Exponent Rule, helps simplify expressions and solve equations rapidly.
headline of the respective core concept
Negative numbers can sometimes be confusing when combined with exponents. It's key to remember that a negative sign outside an exponent remains independent of the exponent's rules.
For example, in the expression \(-6^0\), the exponent zero only applies to the base, which is 6, not the negative sign. This distinction ensures the correct evaluation of expressions.
Applying the Zero Exponent Rule, which states any non-zero number to the power of zero is 1, we consider the expression as \(6^0\). Then we apply the negative sign to the result: \- (6^0) = -1.
headline of the respective core concept
Algebra often involves working with exponents and negative numbers. Recognizing the rules and how they interact is key to solving algebraic problems.
For instance, in the expression \(-6^0\), understanding both the Zero Exponent Rule and how the negative sign functions allows us to simplify it correctly.
This process includes:
  • Identifying the base and exponent
  • Applying the Zero Exponent Rule
  • Recognizing the role of the negative sign independently
By ensuring each step is correctly followed, algebra becomes more approachable and less error-prone.

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