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Chapter 5: Problem 40

Simplify. $$ 2600 \div 13-5^{3} \quad[1.9 \mathrm{c}] $$

Short Answer

Expert verified
75

Step by step solution

01

Division

First, perform the division: \[ 2600 \u00f7 13 \ \text{To calculate this,} \ 2600 \ \text{divided by 13 equals 200.} \ \text{So, we have 200.} \]
02

Exponentiation

Next, calculate the exponentiation part: \[ 5^{3} \ \text{This equals} \ 5 \times 5 \times 5 = 125 \]
03

Subtraction

Finally, subtract the result of the exponentiation from the division result: \[ 200 - 125 = 75 \ \text{Therefore,} \ 2600 \ \text{divided by 13 minus} \ 5^{3} \ \text{equals} \ 75. \]

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Key Concepts

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

Division
Division is a fundamental arithmetic operation. It involves splitting a number into equal parts. For instance, dividing 2600 by 13 means we determine how many times 13 fits into 2600 equally.

  • Understanding Division: Think of division as distributing a quantity evenly. For example, if you have 2600 apples and you want to divide them into 13 groups, you will get 200 apples in each group.
  • How to Perform Division: With basic arithmetic, division can be simplified by using long division or a calculator. For 2600 梅 13, you divide 2600 by 13 to get 200.
Here鈥檚 the operation for reference: 2600 梅 13 = 200.

Once we solve this division, we move to the next step: exponentiation.
Exponentiation
Exponentiation is a mathematical operation that involves raising a number, called the base, to the power of an exponent. It means multiplying the base by itself a certain number of times.

  • Understanding Exponentiation: When you see an expression like 5^{3}, it means you multiply 5 by itself three times: 5 脳 5 脳 5. In other words, it's like repeated multiplication.
  • Performing Exponentiation: Calculate step-by-step: 5 脳 5 = 25 and then, 25 脳 5 = 125.
In our problem, 5^{3} equals 125.

After finding the result of the exponentiation, we proceed to subtraction.
Subtraction
Subtraction is another basic arithmetic operation. It's the process of finding the difference between two numbers. When you subtract, you take away one quantity from another.

  • Understanding Subtraction: Think of subtraction as removing items from a set. For example, if you start with 200 items and remove 125 items, you鈥檙e left with 75 items.
  • How to Perform Subtraction: Align the numbers by place value and subtract from right to left, borrowing if necessary. For 200 - 125, subtract 125 from 200 to get 75.
In our problem, after performing the subtraction, we find that 200 - 125 = 75.

So, when we complete all operations in the expression 2600 梅 13 - 5^{3}, the simplified result is 75.

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Most popular questions from this chapter

Solve. $$ \frac{12}{4}=\frac{x}{3} $$

Use \(<\) or \(>\) for \(\square\) to write a true sentence. \([3.3 \mathrm{~b}]\) $$ \frac{1}{6} \square \frac{2}{11} $$

Determine whether each number is prime, composite, or neither. \([2.1 \mathrm{c}]\) $$ 83 $$

Determine whether each number is prime, composite, or neither. \([2.1 \mathrm{c}]\) $$ 28 $$

Solve. Round the answer to the nearest thousandth. $$ \frac{12.0078}{56.0115}=\frac{789.23}{y} $$
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