/*! 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 78 Evaluate using a calculator. $... [FREE SOLUTION] | 91影视

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Chapter 5: Problem 78

Evaluate using a calculator. $$ (-8)^{4} $$

Short Answer

Expert verified
The value of (-8)^{4} is 4096.

Step by step solution

01

Understand the Problem

Identify the expression that needs to be evaluated: (-8)^{4}
02

Enter the Base

Input the base of the expression into the calculator. In this case, enter -8.
03

Select the Exponentiation Function

Find the exponentiation function on the calculator. This is usually represented by a button labeled with y^x or ^.
04

Enter the Exponent

Input the exponent value, which is 4, into the calculator and execute the operation.
05

Read the Result

The calculator will display the result of (-8)^{4} which is 4096.

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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 raises a number (the base) to the power of another number (the exponent). The expression \((-8)^{4}\) means that -8 (the base) is multiplied by itself 4 times.
This is calculated as: \((-8) \times (-8) \times (-8) \times (-8) = 4096\).
Here are some key points about exponentiation:
  • It is repeated multiplication.
  • The base can be any real number, positive or negative.
  • The exponent tells us how many times to multiply the base by itself.
Understanding these basics helps in solving exponentiation problems easily.
Using a Calculator
A calculator can make exponentiation tasks much simpler and faster. Here鈥檚 how you can use a calculator to evaluate \((-8)^{4}\):
  • First, input the base, which is -8.
  • Next, find the exponentiation function. This button may be labeled \('y^x'\) or \('^'\), depending on your calculator model.
  • After selecting the exponentiation function, enter the exponent number, in this case, 4.
  • Finally, execute the operation by pressing the \('=\) button, and read the displayed result, which should be 4096.
Using this process ensures you get accurate results quickly and efficiently.
Step-by-Step Problem Solving
Let鈥檚 break down the problem-solving process step by step to ensure understanding:
  • **Step 1: Understand the Problem**: Recognize that you need to evaluate \( (-8)^{4} \), which involves exponentiation.
  • **Step 2: Enter the Base**: Start by inputting the base number, -8, into the calculator.
  • **Step 3: Select the Exponentiation Function**: Locate and press the exponentiation function button ( \('y^x'\) or \('^'\) ).
  • **Step 4: Enter the Exponent and Execute the Operation**: Enter the exponent value, 4, and execute the operation.
  • **Step 5: Read the Result**: View and note the result, which is 4096.
Practicing these steps improves your ability to handle similar problems in the future with confidence.

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