Problem 99 Describe what it means to raise ... [FREE SOLUTION]

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College Algebra

Robert Blitzer

$Math Studyset 91影视 Explanations$ Math

3 Edition

Chapter 0: Problem 99

Describe what it means to raise a number to a power. In your description, include a discussion of the difference between $-5^{2}$ and $(-5)^{2}$

Short Answer

Expert verified

Raising a number to a power means multiplying it by itself a certain number of times specified by the power. The difference between $-5^{2}$ and $(-5)^{2}$ lies in the order of operations. Without parentheses, exponentiation is performed first and negation afterwards, leading to $-25$. With parentheses, $-5$ is squared, resulting in $+25$.

Step by step solution

Explanation of raising a number to a power

Raising a number to a power, also known as exponentiation, refers to the operation of multiplying the number by itself for the number of times specified by the power. For instance, raising 3 to the power of 2 (written as $3^{2}$) means multiplying 3 by itself, which equals 9.

Difference between $-5^{2}$ and $(-5)^{2}$

The difference between $-5^{2}$ and $(-5)^{2}$ lies in the order of operations. In $-5^{2}$, the exponentiation comes first, followed by the negation. Thus, $-5^{2}$ is computed as $- (5 * 5)$, which equals $-25$. On the other hand, $(-5)^{2}$ involves squaring the number $-5$, so it is computed as $-5 * -5$, which equals $+25$. The parentheses change the order of the operations.

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91影视

Describe what it means to raise a number to a power. In your description, include a discussion of the difference between \(-5^{2}\) and \((-5)^{2}\)

Short Answer

Step by step solution

Explanation of raising a number to a power

Difference between \(-5^{2}\) and \((-5)^{2}\)

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