/*! 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 52 \(\frac{2^{2}+4^{2}}{5}\)... [FREE SOLUTION] | 91影视

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Chapter 1: Problem 52

\(\frac{2^{2}+4^{2}}{5}\)

Short Answer

Expert verified
The solution to the given mathematical expression is 4.

Step by step solution

01

Exponentiation

Start by calculating the exponent for each component within the brackets: \(2^2 = 4\) and \(4^2 = 16\).
02

Addition

Next, add the results of the two exponentiations together: \(4 + 16 = 20\).
03

Division

Finally, divide the result of the addition by 5: \(20 梅 5 = 4\).

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Key Concepts

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

Exponentiation
Exponentiation is a powerful operation in mathematics that deals with raising a number, known as the base, to a certain power, referred to as the exponent. The exponent tells us how many times we need to multiply the base by itself.
  • For instance, in the expression \(2^2\), the base is 2 and the exponent is 2. Thus, we calculate it as \(2 \times 2 = 4\).
  • Similarly, for \(4^2\), the base 4 is raised to the power of 2, which means \(4 \times 4 = 16\).
Exponentiation simplifies repeated multiplication, making calculations quicker and easier. Remember, any number raised to the power of zero is always 1. Also, keep in mind when exponentiation is part of a larger expression, it's typically calculated first, following the order of operations.
Order of Operations
The order of operations is a fundamental concept in mathematics that determines the correct sequence of steps used to evaluate a math expression. This sequence is often remembered by the acronym PEMDAS:
  • Parentheses
  • Exponents
  • Multiplication and Division (from left to right)
  • Addition and Subtraction (from left to right)
In our example exercise, we first handle the exponentiations: \(2^2\) and \(4^2\). After calculating these, we move to the addition of the results \(4 + 16\). Finally, the division \(\frac{20}{5}\) concludes the evaluation. Following the order of operations ensures that every mathematical expression is solved correctly and consistently.
Division in Algebra
Division in algebra is the operation of distributing a quantity into equal parts. In the expression \(\frac{2^2 + 4^2}{5}\), division is the final step completed after exponentiation and addition. Once we have the sum of the exponents \(20\), we divide by the coefficient, which in this scenario is 5.
  • The result is obtained by dividing 20 into 5 equal parts, calculated as \(20 \div 5 = 4\).
It's important to perform division carefully, especially in more complex expressions. Division can often introduce fractions, which need special attention. Understanding how division interacts with other operations, like multiplication and addition, is essential for solving algebraic expressions effectively.

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Most popular questions from this chapter

Understanding Exponents Which part of the exponential expression \(2^{4}\) is the base? Which part is the exponent?

\(\frac{0}{6^{2}+1}\)

Cooking You make 60 ounces of dough for breadsticks. Each breadstick requires \(\frac{5}{4}\) ounces of dough. How many breadsticks can you make?

\(\frac{1-3^{2}}{-2}\)

Finding Inverses Find (a) the additive inverse and (b) the multiplicative inverse of \(-8\).
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