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Chapter 4: Problem 30

Evaluate. Assume that all variables represent nonzero real numbers. $$ (-30)^{0} $$

Short Answer

Expert verified
\( -30^{0} = 1 \)

Step by step solution

01

Understand the Zero Exponent Rule

Any non-zero number raised to the power of zero is equal to one. This concept is known as the zero exponent rule.
02

Apply the Rule

Given the expression \( -30^{0} \), apply the zero exponent rule by recognizing that \( -30 \) is a non-zero number.
03

Simplify

According to the zero exponent rule, \( -30^{0} = 1 \).

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Key Concepts

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

Exponentiation
Exponentiation is the operation of raising one number, called the base, to the power of another number, called the exponent. The exponent tells you how many times the base is multiplied by itself. For example, in the expression \( 3^4 \), 3 is the base and 4 is the exponent, meaning 3 is multiplied by itself 4 times: \( 3 \times 3 \times 3 \times 3 \).
Understanding exponentiation is crucial for simplifying expressions and solving equations involving powers. It's a fundamental concept in algebra and beyond.
Properties of Exponents
The properties of exponents help simplify expressions and solve equations. Some of the core properties include:
  • Product of Powers: \( a^m \times a^n = a^{m+n} \)
  • Quotient of Powers: \( \frac{a^m}{a^n} = a^{m-n} \)
  • Power of a Power: \( (a^m)^n = a^{mn} \)
  • Power of a Product: \( (ab)^n = a^n \times b^n \)
  • Zero Exponent Rule: \( a^0 = 1 \) for any non-zero \( a \)
These properties allow you to manipulate and simplify expressions involving exponents easily. The Zero Exponent Rule is particularly useful when simplifying expressions like \( (-30)^0 \).
Simplification of Expressions
Simplifying expressions involves using algebraic rules to make them easier to understand or solve. When dealing with exponents, you often use properties of exponents. For example, in the expression \( (-30)^0 \), you apply the Zero Exponent Rule, which states that any non-zero number raised to the power of zero is one. So, simplifying \( (-30)^0 \) results in 1.
Always check for opportunities to apply these rules for simplification. Doing so can make calculations and problem-solving much more manageable. Practice with these rules will help you become more comfortable with algebraic expressions.

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Most popular questions from this chapter

Write using only positive exponents and then evaluate. Assume that all variables represent nonzero real numbers. $$ \left(\frac{4}{5}\right)^{-2} $$

Find each product. $$ (3 r+2 s)\left(r^{3}+2 r^{2} s-r s^{2}+2 s^{3}\right) $$

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