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Chapter 4: Problem 7

\(1-5^{0}\)

Short Answer

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Step by step solution

01

- Understanding Exponents

Remember that any number raised to the power of 0 is equal to 1. That is, for any number x, \[x^0 = 1\].
02

- Simplify the Exponent

Apply the rule from Step 1 to simplify \(5^0\). Since \(5^0 = 1\), we can write \[1 - 5^0 = 1 - 1\].
03

- Perform the Subtraction

Now perform the subtraction: \[1 - 1 = 0\].

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Key Concepts

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

zero exponent rule
In mathematics, there is a fundamental rule known as the zero exponent rule. This rule states that any nonzero number raised to the power of zero is equal to one. Mathematically, it is expressed as \(x^0 = 1\) where \(x\) is any nonzero number. For example, \(5^0 = 1\), \(10^0 = 1\), and even \((-3)^0 = 1\). This rule is crucial when simplifying expressions that involve exponents. By understanding and applying this simple rule, you can easily tackle various math problems. Always remember, no matter the base, if the exponent is zero, the result is one.
simplifying exponents
When working with exponents, simplifying them is an essential skill. Simplifying means making the expression as straightforward as possible. Let's consider the expression \(5^0\). By using the zero exponent rule, we know that \(5^0 = 1\). Now, if an expression involves multiple steps, like \(1 - 5^0\) in the exercise, you simplify the exponent part first, then proceed to simplify the entire expression.
Steps to simplify exponents:
  • Identify parts of the expression that involve exponents.
  • Apply relevant exponent rules, like the zero exponent rule.
  • Simplify the expression step-by-step.
For our specific example: \[1 - 5^0\] Apply the zero exponent rule: \[1 - 1\] Simplify: \[1 - 1 = 0\] By following each step carefully, simplifying exponents becomes more manageable.
basic arithmetic operations
Basic arithmetic operations are the foundation of most math problems. These include addition, subtraction, multiplication, and division. In the given exercise, we encounter subtraction, which is an essential operation to master.
Let's break down the exercise:
  • The original problem is \(1 - 5^0\).
  • Using the zero exponent rule, simplify \(5^0 = 1\).
  • The expression now becomes \[1 - 1\].
Finally, perform the subtraction: \[1 - 1 = 0\]. This shows how effectively understanding and applying basic arithmetic, along with exponent rules, can simplify and solve math problems efficiently. Never overlook the importance of these fundamental operations as they are the backbone of all more complex mathematical concepts.

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Most popular questions from this chapter

Add or subtract as indicated. \(\left(2 c^{4} d+3 c^{2} d^{2}-4 d^{2}\right)-\left(c^{4} d+8 c^{2} d^{2}-5 d^{2}\right)\)

Perform each indicated operation. \(\left[\left(8 m^{2}+4 m-7\right)-\left(2 m^{2}-5 m+2\right)\right]-\left(m^{2}+m+1\right)\)

Find each product. Recall that \(a^{2}=a \cdot a\) and \(a^{3}=a^{2} \cdot a\). $$ \left(2 x^{2}+\frac{2}{3} y\right)\left(3 x^{2}-\frac{3}{4} y\right) $$

Find each product. Recall that \(a^{2}=a \cdot a\) and \(a^{3}=a^{2} \cdot a\). $$ 5(3 k-7)(5 k+2) $$

Find each product. Recall that \(a^{2}=a \cdot a\) and \(a^{3}=a^{2} \cdot a\). $$ -3 a(3 a+1)(a-4) $$
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