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Chapter 3: Problem 87

Evaluate each expression. $$ 5 \cdot 5 \cdot 5 \cdot 5 $$

Short Answer

Expert verified
625

Step by step solution

01

Identify the Repetition

Notice that the number 5 is repeated four times in the expression.
02

Express as an Exponent

Rewrite the repeated multiplication using an exponent: \[ 5 \times 5 \times 5 \times 5 = 5^4 \]
03

Calculate the Exponent

Evaluate the exponent: \[ 5^4 = 5 \times 5 \times 5 \times 5 = 625 \]

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Key Concepts

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

Repeated Multiplication
Repeated multiplication is a basic and essential concept in mathematics. It involves multiplying the same number by itself multiple times.
For example, if you have 5 multiplied by itself four times, the expression is: 5 鈰� 5 鈰� 5 鈰� 5.
Repeated multiplication can be tedious when the number is repeated many times, which is why we use exponentiation as a convenient shorthand.
Exponentiation
Exponentiation is the process of raising a number, called the base, to a power, which is an exponent. The exponent tells us how many times we multiply the base by itself.
For instance, in the expression 5^4, the base is 5 and the exponent is 4.
This means we multiply 5 by itself four times:
  • Step 1: 5 鈰� 5 = 25
  • Step 2: 25 鈰� 5 = 125
  • Step 3: 125 鈰� 5 = 625

So, 5^4 equals 625.
Exponentiation allows us to write and compute large repeated multiplication expressions more easily.
Basic Algebra
Basic algebra involves understanding and manipulating mathematical expressions involving variables, numbers, and operation symbols.
In algebra, we often see the use of exponents as they simplify repeated multiplication.
Identifying patterns and rewriting them using exponents is a key algebraic skill. For example, recognizing 5 鈰� 5 鈰� 5 鈰� 5 as 5^4 is an application of algebraic principles.
This skill helps solve complex problems efficiently. By mastering basic algebra and exponentiation, you can handle more advanced mathematical topics.

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Most popular questions from this chapter

Write an equation for each line passing through the given point and having the given slope. Give the final answer in slope-intercept form. $$ (7,-2), m=-\frac{7}{2} $$

Write an equation for each line passing through the given pair of points. Give the final answer in (a) slope-intercept form and (b) standard form. $$ (-2,-1) \text { and }(3,-4) $$

Evaluate each expression. $$ 3 \cdot 3 \cdot 3 $$

Graph each line passing through the given point and having the given slope. $$ (-1,4), m=\frac{2}{5} $$

Do \((3,4)\) and \((4,3)\) correspond to the same point in the plane? Explain.
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