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Chapter 10: Problem 24

Simplify. $$7 y^{0}$$

Short Answer

Expert verified
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Step by step solution

01

Recall the Zero Exponent Rule

Any non-zero number raised to the power of zero is equal to one. This means that for any number or variable x, we have: \( x^0 = 1 \)
02

Apply the Zero Exponent Rule

In this problem, you have \( y^0 \). According to the zero exponent rule, \( y^0 \) is equal to 1.
03

Simplify the Expression

Now replace \( y^0 \) with 1 in the original expression: \( 7 y^0 = 7 \times 1 \). Therefore, \( 7 y^0 = 7 \).

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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 fundamental concept in algebra. It may seem confusing at first, but it's pretty straightforward. The rule states that any number or variable raised to the zero power is equal to one. Period.
Let's break this down with an example: If you have any non-zero number, say 5, and you raise it to the power of zero, it becomes 1. Mathematically, it's written as: \[ 5^0 = 1 \]
This rule is true for any number or variable. So, if you have a variable like \( x \), then:\[ x^0 = 1 \]
This is super useful when simplifying expressions in algebra.
Exponentiation
Exponentiation is the operation of raising a number to the power of an exponent. The notation for this is often written as \( a^n \), where \( a \) is the base and \( n \) is the exponent.
Here's a quick breakdown of common exponent rules:
  • If the exponent is 1, the number stays the same: \( a^1 = a \)
  • An exponent of 0 makes the base equal to 1: \( a^0 = 1 \)
  • With a negative exponent, you flip the base: \( a^{-n} = \frac{1}{a^n} \)
Understanding these basic principles of exponentiation is key to making algebraic simplifications.
Simplifying Algebraic Expressions
Simplifying algebraic expressions involves making the expression as simple as possible. This often means following a set of rules and procedures.
Let's look at a step-by-step process for simplifying the expression \( 7y^0 \):
First, recall the zero exponent rule: Any number raised to the zero power is 1. So, \( y^0 = 1 \).
Second, replace \( y^0 \) with 1 in the original expression: \( 7y^0 \) becomes \( 7 \times 1 \).
Finally, perform the multiplication: \( 7 \times 1 = 7 \).
The simplified form of \( 7y^0 \) is thus 7. This technique can be applied to more complicated expressions as long as you follow the basic rules.

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Most popular questions from this chapter

The cost (in dollars) for a speeding ticket is given by the polynomial \(110+15 x .\) In this context, \(x\) is the number of miles per hour a motorist travels over the speed limit. a. Evaluate the polynomial for \(x=15\) and interpret the answer in the context of this problem. b. Evaluate the polynomial for \(x=25\) and interpret the answer in the context of this problem.

Which is greater? \(\left(4^{4}\right)^{5}\) or \(\left(4^{5}\right)^{4}\)

Simplify. Write the answers with positive exponents only. $$\frac{x^{5}}{x^{-7}}$$

$$\text { Fill in the blanks }\left(x^{3}\right)^{5}=x \square \cdot \square=x^{15}$$

Simplify. Write the answer with positive exponents only. $$\frac{m^{-1} n^{7}}{p^{-3}}$$
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