/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 35 Evaluate each expression. $$ ... [FREE SOLUTION] | 91影视

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Chapter 0: Problem 35

Evaluate each expression. $$ -3^{6} $$

Short Answer

Expert verified
-729.

Step by step solution

01

Understand the expression

The expression is given as \( -3^{6} \). It is important to recognize that the exponentiation process will be applied to 3 first, and then the result will be multiplied by -1.
02

Calculate the power of 3

Calculate \( 3^{6} \). This means multiplying 3 by itself 6 times: \[ 3 \times 3 \times 3 \times 3 \times 3 \times 3 = 729 \]
03

Apply the negative sign

Once you have \( 3^{6} = 729 \), apply the negative sign in front of the result: \[ - 729 \]

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Key Concepts

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

Exponentiation
Exponentiation is a mathematical operation that involves raising a number to a power. This means multiplying the number by itself a specified number of times.

In the exercise \( -3^{6} \), the exponent is 6, and the base is 3. To evaluate this:
  • Raise 3 to the power of 6: \[ 3^{6} \]
  • Multiply 3 by itself 6 times:

    \[ 3 \times 3 \times 3 \times 3 \times 3 \times 3 = 729 \]
It's important to understand that exponentiation has higher precedence in the order of operations, so it is calculated before other operations like multiplication or addition.
Negative Numbers
Negative numbers can sometimes be confusing, especially when dealing with exponentiation. In our exercise, \( -3^{6} \), the negative sign is outside of the exponentiation, which means it鈥檚 not part of the base.

Here's how it breaks down:
  • First, raise 3 to the power of 6:
    \[ 3^{6} = 729 \]
  • Then, apply the negative sign to the result:
    \[ -729 \]
This ensures the final answer accounts for the initial negative sign as a multiplier.
Order of Operations
Understanding the order of operations is crucial to correctly evaluating expressions. The commonly used acronym PEMDAS can help:
  • P - Parentheses
  • E - Exponents
  • M/D - Multiplication and Division (from left to right)
  • A/S - Addition and Subtraction (from left to right)
In our exercise \( -3^{6} \), applying the order of operations, exponentiation comes before multiplication by -1:
  • Perform the exponentiation first:
    \[ 3^{6} = 729 \]
  • Then apply the negative sign:
    \[ -729 \]
Getting the order right ensures accurate results in more complex problems.

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Most popular questions from this chapter

Use an inequality symbol to write each statement. $$ 5+0 \text { is not equal to } 0 $$

Evaluate each expression for \(w=4, x=-\frac{3}{4}, y=\frac{1}{2},\) and \(z=1.25 .\) $$ w z-12 y $$

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Find each square root. If it is not a real number, say so. $$ \sqrt{\frac{100}{121}} $$

Simplify each expression. $$ -14\left(-\frac{2}{7}\right) \div(2 \cdot 6-10) $$
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