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Chapter 5: Problem 34

Assume that all variables represent nonzero real numbers. $$ -8^{0}-k^{0} $$

Short Answer

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Step by step solution

01

- Understand the Zero Exponent Rule

Recall that any nonzero real number raised to the power of 0 equals 1. Therefore, for any nonzero real number x, we have \[ x^0 = 1. \]
02

- Apply the Zero Exponent Rule to Each Term

Identify the terms with exponents in the given expression \(-8^0 - k^0\). Apply the zero exponent rule to each term individually: \[ -8^0 = 1 \] and \[ k^0 = 1. \]
03

- Simplify the Expression

Rewrite the expression by replacing each term with 1: \[ -8^0 - k^0 = 1 - 1. \] Then simplify the resulting expression: \[ 1 - 1 = 0. \]

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Key Concepts

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

Exponent Rules
Exponent rules help simplify expressions that involve powers of numbers or variables. One important rule is the Zero Exponent Rule. This rule states that any nonzero number raised to the power of zero equals one: \[ x^0 = 1.\]

The Zero Exponent Rule works for all nonzero numbers, which includes both positive and negative numbers, as well as variables.

Remembering this rule can make solving algebraic expressions much easier and less intimidating.
Simplifying Expressions
Simplifying expressions in mathematics means to make them easier to understand and work with.

In our exercise, the expression -8^0 - k^0 can be simplified by applying the Zero Exponent Rule. First, understand that \[ -8^0 = 1 \] and \[ k^0 = 1.\]

Now, substitute these values back into the expression: \[ 1 - 1.\]

Lastly, perform the simple arithmetic to get the final simplified result: \[ 1 - 1 = 0. \]

Breaking down the steps and following the rules like this makes it easier to handle even complicated expressions.
Intermediate Algebra
Intermediate algebra deals with more complex operations than basic algebra. It includes working with exponents, simplifying expressions, and solving equations.

Understanding core concepts like the Zero Exponent Rule helps in tackling intermediate algebra problems efficiently.

To excel in intermediate algebra, you should:
  • Master basic exponent rules
  • Practice simplifying expressions step by step
  • Apply rules methodically


These strategies will build a strong foundation for advanced mathematical concepts.

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Most popular questions from this chapter

Solve each problem. In \(2009,\) the population of Costa Rica was approximately \(4.25 \times 10^{6} .\) The population density was 83.3 people per square kilometer. (a) Write the population density in scientific notation. (b) To the nearest square kilometer, what is the area of Costa Rica?

Find each product. $$ (3+x+y)(-3+x-y) $$

Write each number in scientific notation. $$ 0.00000692 $$

Write each number in scientific notation. $$ 0.0072 $$

Solve each problem. In January 2010 , the population of the United States was approximately 308.4 million. (a) Write the January 2010 population using scientific notation. (b) Write \(S 1\) trillion, that is, \(\$ 1,000,000,000,000,\) using scientific notation. (c) Using your answers from parts (a) and (b), calculate how much each person in the United States in the year 2010 would have had to contribute in order to make someone a trillionaire. Write this amount in standard notation to the nearest dollar.
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