Problem 10 Evaluate. $$-(-7)^{0}$$... [FREE SOLUTION]

Chapter 2: Problem 10

Evaluate. $$-(-7)^{0}$$

Short Answer

Expert verified

The value of the expression $-(-7)^{0}$ is $-1$.

Step by step solution

Recall that any number raised to the power of 0 is equal to 1. Therefore, $(-7)^{0} = 1$ #Step 2: Apply the negative sign outside the bracket#

Our expression becomes $-1$, as we were asked to evaluate $-(-7)^{0} = -1$. So, the value of the expression $-(-7)^{0}$ is $-1$.

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Key Concepts

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

Exponentiation

Exponentiation is an essential mathematical concept used to express repeated multiplication of the same number. For instance, when we say "3 squared" or "3 raised to the power of 2" and write it as $3^2$, it means multiplying 3 by itself: $3 \times 3 = 9$.

The base is the number being multiplied.
The exponent indicates how many times the base is used as a factor.

When the base is negative and the exponent is even, the result is positive, such as $(-2)^2 = 4$. If the exponent is odd, the result is negative, like $(-2)^3 = -8$. However, this concept is zeroed out when we discuss zero exponent in the next sections.

Negative Numbers

Negative numbers are those less than zero, indicated by a minus (-) sign. When dealing with operations involving negative numbers, it is crucial to consider these rules:

Multiplying or dividing two negative numbers yields a positive result.
Multiplying or dividing a positive number by a negative number results in a negative value.
Adding and subtracting negative numbers involves considering their direction on a number line. For instance, $ -3 + 2 $ results in $-1$.

In our given problem, the negative sign in front of the expression $(-7)^0$ needs to be carefully considered as it affects the overall result when combined with the zero exponent.

Zero Exponent Rule

The Zero Exponent Rule is an interesting mathematical property that states any non-zero base raised to the power of zero is equal to 1. Simply put, $a^0 = 1$ if $a eq 0$. Why does this work? Well, consider the pattern of powers of a number decreasing:

$a^3 = a \times a \times a$
$a^2 = a \times a$
$a^1 = a$
So naturally, $a^0 = 1$, following one less multiplication.

Applying this rule to $(-7)^0$ in our exercise, we get $(-7)^0 = 1$, as long as $-7$ is not zero, which it isn't. Hence, understand that despite whatever value the base has, if it鈥檚 non-zero, the expression's value remains 1. This property is vital in simplifying expressions easily.

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91影视

Evaluate. $$-(-7)^{0}$$

Short Answer

Step by step solution

Recall that any number raised to the power of 0 is equal to 1. Therefore, \((-7)^{0} = 1\) #Step 2: Apply the negative sign outside the bracket#

Key Concepts

Exponentiation

Negative Numbers

Zero Exponent Rule

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