Write 10x10x10x10x10x10 as an exponent
The Correct Answer and Explanation is:
To express (10 \times 10 \times 10 \times 10 \times 10 \times 10) in exponential notation, we recognize that multiplying the same number by itself multiple times can be represented using exponents. In this case, since the number (10) is being multiplied together (6) times, we can write it as:
[
10^6
]
Calculation of (10^6)
To understand the value of (10^6), we calculate it as follows:
[
10^6 = 10 \times 10 \times 10 \times 10 \times 10 \times 10
]
Now let’s break down this multiplication step-by-step:
- First Pair: (10 \times 10 = 100)
- Second Pair: (100 \times 10 = 1,000)
- Third Pair: (1,000 \times 10 = 10,000)
- Fourth Pair: (10,000 \times 10 = 100,000)
Thus, we can summarize the multiplication:
- (10^1 = 10)
- (10^2 = 100)
- (10^3 = 1,000)
- (10^4 = 10,000)
- (10^5 = 100,000)
- (10^6 = 1,000,000)
Therefore, the final answer is:
[
10^6 = 1,000,000
]
Explanation of Exponents
Exponents are a shorthand way to indicate repeated multiplication of a number by itself. The base number (in this case, (10)) is raised to an exponent (the superscript number, (6)), which indicates how many times the base is multiplied by itself. This notation simplifies mathematical expressions and calculations, especially when dealing with large numbers.
Using exponents is particularly helpful in scientific notation and calculations involving powers of ten, which are commonplace in fields such as physics, engineering, and finance. For example, in scientific notation, (10^6) is often used to represent one million, making it easier to read and compare large values. Understanding how to manipulate and calculate with exponents is crucial in advanced mathematics and its applications across various disciplines.