Problem 1 Simplify. $$ a^{0}, \text { ... [FREE SOLUTION]

Chapter 15: Problem 1

Simplify. $$ a^{0}, \text { for } a=-25 $$

Short Answer

Expert verified

Any non-zero number to the power of 0 is 1, so \[ (-25)^0 = 1 \].

Step by step solution

Identify the Property

Recall the property of exponents that any non-zero number raised to the power of 0 equals 1. Mathematically, this is written as: \[ a^0 = 1 \] for any $ a eq 0 $.

Apply the Property to the Given Expression

Since $ a = -25 $, apply the exponent property $ a^0 $: \[ (-25)^0 = 1 \]

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Key Concepts

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

Zero Exponent Rule

Let's dive into the Zero Exponent Rule. This rule states that any number, except zero, raised to the power of zero equals one. This might seem confusing at first, but it's a key property in algebra.
Let's break it down:

When a number is raised to a power, the exponent tells us how many times to multiply the base by itself.
For example, $3^2 = 3 \times 3 = 9$.
But if the exponent is zero, we're essentially multiplying by nothing, and the result is always 1.

This rule is useful when simplifying expressions and solving equations. So, for our number $-25$, applying the zero exponent rule gives us:
\[ (-25)^0 = 1 \]
Simple, right?

Simplifying Expressions

When dealing with expressions involving exponents, simplification is crucial. Simplifying helps to make the expression easier to understand and work with. Here are a few tips:

First, identify any exponent rules that you can apply. In our example, the zero exponent rule was key.
Apply the rule to the components of the expression. If we have multiple terms, we simplify each one according to its rules.
Combine like terms and simplify any further if possible.

In the given exercise, we have the expression $(-25)^0$. By directly applying the zero exponent rule, we simplify it to 1.
Notice how this makes the expression much simpler and easier to handle.

Properties of Exponents

Understanding the properties of exponents is essential for simplifying expressions and solving problems. The key properties include:

Product of Powers: $a^m \times a^n = a^{m+n}$. Multiply by adding exponents.
Power of a Power: $(a^m)^n = a^{m \times n}$. Multiply the exponents.
Quotient of Powers: $\frac{a^m}{a^n} = a^{m-n}$. Subtract the exponents when dividing.
Zero Exponent Rule: $a^0 = 1$ for any non-zero $a$.
Negative Exponent Rule: $a^{-n} = \frac{1}{a^n}$. Flip the base and make the exponent positive.

In our example, we specifically used the zero exponent rule. Remember, these properties help us tackle even the most complex expressions by breaking them down step by step.

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91影视

Simplify. $$ a^{0}, \text { for } a=-25 $$

Short Answer

Step by step solution

Identify the Property

Apply the Property to the Given Expression

Key Concepts

Zero Exponent Rule

Simplifying Expressions

Properties of Exponents

One App. One Place for Learning.

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