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Chapter 1: Problem 37

Write each expression without using exponents and find the value of each expression $$6^{2}$$

Short Answer

Expert verified
The expression \(6^{2}\) without exponents is \(6 * 6\), and the value of this expression is 36.

Step by step solution

01

Understand the Exponential Expression

The exponential expression \(6^{2}\) means the number 6 is being multiplied by itself - or, in other words, there are 2 factors of 6. This can be written as \(6 * 6\).
02

Perform the Multiplication

Next, multiply the 2 factors of 6 together: \(6 * 6 = 36\).

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Key Concepts

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

Exponential Expression
An exponential expression is a mathematical way to express repeated multiplication of a number by itself. In the expression \(6^{2}\), the number 6 is known as the base, and the small number 2 written as a superscript is called the exponent. This tells us how many times the base (6) is multiplied by itself.

Breaking down the exponential expression \(6^{2}\), we can interpret it in a few simple steps:
  • The base number: 6
  • The exponent: 2
  • Meaning: Multiply 6 by itself 2 times
Exponential expressions simplify dealing with large numbers and operations involving repeated multiplication, making mathematical calculations more efficient and manageable.
Multiplication
Multiplication is one of the basic arithmetic operations, which involves the process of adding a number to itself a certain number of times. In the context of an exponential expression, multiplication is the action we perform based on the given exponent.
Let's delve deeper into the multiplication seen in \(6^{2}\):
  • Read \(6^{2}\) as "6 multiplied by itself 2 times".
  • Construct the multiplication sequence: \(6 \times 6\).
  • Perform the operation: \(6 \times 6\) results in 36.
By understanding the connection between exponents and multiplication, we can easily break down these expressions into straightforward, manageable calculations.
Factors
The term 'factors' refers to numbers we multiply to get another number. In the context of our exercise, the factors of the expression \(6^{2}\) are each of the 6鈥檚 present in the multiplication form of the expression.

Here's how it works with \(6^{2}\):
  • When we expand \(6^{2}\), we write it as \(6 \times 6\).
  • These two 6鈥檚 are the factors of the expression.
  • Multiply these factors together: \(6 \times 6\) gives 36, which is the final value of the expression.
Understanding factors in exponential expressions allows us to visualize how numbers grow through multiplication, simplifying complex problems into simple computations.

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