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Chapter 5: Problem 52

Simplify. \(7 m^{0}\) when \(m=1.7\)

Short Answer

Expert verified
The simplified expression is 7.

Step by step solution

01

Understand the Zero Exponent Rule

The zero exponent rule states that any non-zero base raised to the power of zero is equal to one. In mathematical terms, this is expressed as \[ a^0 = 1 \] where \(a\) is any non-zero number. Therefore, \(m^0 = 1\) for any \(m eq 0\).
02

Apply the Zero Exponent Rule

Given the expression \(7 m^0\), we know that \(m^0 = 1\), regardless of the value of \(m\). Therefore, we can simplify the expression by replacing \(m^0\) with \(1\): \[ 7 m^0 = 7 \times 1 \]
03

Simplify the Expression

Now, we simplify the multiplication: \[ 7 \times 1 = 7 \] Hence, the simplified expression is \(7\).
04

Confirm the Value of \(m\)

The value of \(m\) does not affect the simplification since \(m^0 = 1\) regardless. Given that \(m = 1.7\), it is a non-zero number, validating our application of the zero exponent rule.

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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. According to this rule, any non-zero number raised to the power of zero is equal to one. This can be written as \[ a^0 = 1 \]Where \(a\) is any non-zero number. This might seem tricky initially, but think of it as a way to normalize values. For example, if we have \( m^0 \), regardless of what \(m\) is, as long as it isn't zero, the value of \( m^0 \) will always be 1.
Exponents in Algebra
Exponents are a way to represent repeated multiplication of a base number. For instance, \(3^2\) means \(3\) multiplied by itself: \[ 3^2 = 3 \times 3 = 9 \]In algebra, understanding how exponents work is crucial because they often simplify complex calculations and expressions. You can think of exponents as a shorthand to save time and space when writing algebraic expressions. The rules governing exponents, like the zero exponent rule, help to keep these simplifications consistent. Always remember to apply the rules step by step when simplifying expressions involving exponents.
Simplification Process
Simplifying algebraic expressions is about making them easier to work with or understand while maintaining their equivalence. When we see an expression such as \( 7 m^0 \) and know the zero exponent rule, we realize that it simplifies to \( 7 \times 1 \). So, \[ 7 m^0 = 7 \times 1 = 7 \]The value of \(m\) does not affect the outcome because \( m^0 = 1 \). Simplification involves factors like these rules to make expressions more manageable. Breaking down the expressions into basic components, applying the rules, and then reassembling can help achieve the simplified form efficiently.

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Most popular questions from this chapter

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