What is 6x6x6x6 written in exponential notation
The Correct Answer and Explanation is :
The expression ( 6 \times 6 \times 6 \times 6 ) can be written in exponential notation as ( 6^4 ).
Explanation:
Exponential notation is a mathematical way to express repeated multiplication of the same number. In exponential notation, a number (called the base) is raised to a power (called the exponent) that indicates how many times the base is multiplied by itself.
In the case of ( 6 \times 6 \times 6 \times 6 ):
- Identify the base: Here, the base is ( 6 ) because it is the number being multiplied repeatedly.
- Count the factors: The expression contains four factors of ( 6 ). This means that we are multiplying ( 6 ) by itself four times.
- Write in exponential form: The repeated multiplication can be compactly expressed as ( 6^4 ). In this expression, the “4” is the exponent that signifies that the base ( 6 ) is used four times in multiplication.
Benefits of Exponential Notation:
Using exponential notation simplifies expressions and calculations, especially when dealing with large numbers or when a number is multiplied by itself many times. For example, instead of writing out ( 6 \times 6 \times 6 \times 6 ), we can quickly refer to it as ( 6^4 ), which is easier to read and understand.
Additionally, exponential notation is useful in many areas of mathematics and science, such as algebra, calculus, and physics. It helps in solving equations, performing calculations with large numbers, and expressing mathematical concepts in a concise manner.
Calculation:
If you want to calculate ( 6^4 ), you would perform the multiplication as follows:
[
6^4 = 6 \times 6 \times 6 \times 6 = 36 \times 6 \times 6 = 216 \times 6 = 1296.
]
Thus, ( 6^4 = 1296 ).