Simplify 3 to the power of 3
The Correct Answer and Explanation is:
To simplify (3^3), we calculate:
[
3^3 = 3 \times 3 \times 3 = 27
]
The expression (3^3) means “3 raised to the power of 3.” This indicates that the number 3 is multiplied by itself a total of three times. Exponentiation is a mathematical operation involving two numbers: the base and the exponent. In this case, 3 is the base, and 3 is also the exponent. The exponent tells us how many times to multiply the base by itself.
When simplifying powers like (3^3), it helps to think of it step by step:
- First Multiplication: Start with the base. Multiply 3 by itself:
[
3 \times 3 = 9
] - Second Multiplication: Take the result from the first step and multiply it by 3 again:
[
9 \times 3 = 27
]
Thus, (3^3 = 27).
In general, exponents make it easier to express repeated multiplication. Instead of writing (3 \times 3 \times 3), we can simply write (3^3), which is more concise and manageable, especially for larger exponents.
Exponentiation is a fundamental concept in mathematics, widely used in various fields such as science, engineering, and finance. It is particularly important when dealing with exponential growth or decay, like population growth or radioactive decay. Additionally, exponents appear frequently in algebra, simplifying equations and expressions.
In this case, since the exponent is 3, the operation involved is straightforward, but understanding how to manage exponents helps in solving more complex problems.