Select the correct answer.
How would you write 6 × 6 × 6 × 6 as an exponential expression?
The Correct Answer and Explanation is:
The correct answer is:
6⁴
Explanation:
When asked to express a repeated multiplication as an exponential expression, we can use the concept of exponents, also known as powers. An exponent is a shorthand way of expressing repeated multiplication of the same number.
In the given expression, we have:
6 × 6 × 6 × 6.
This is a multiplication of the number 6, repeated four times. In exponential notation, this repeated multiplication is written as:
6⁴.
Here’s a breakdown of what this means:
- The base (6) is the number being multiplied.
- The exponent (4) tells us how many times the base (6) is being multiplied by itself.
In general, the rule for exponents is as follows:
a × a × a × … × a (n times) = aⁿ.
So, in this case:
- We have 6 multiplied by itself four times, so we write it as 6 raised to the power of 4, or 6⁴.
Why Use Exponents?
Using exponents simplifies the writing of long multiplication expressions and makes calculations easier to work with. For example, multiplying numbers like 6 × 6 × 6 × 6 without using exponents would take more space and require additional effort to compute. However, with 6⁴, it is immediately clear that we are multiplying the number 6 by itself four times.
Exponential expressions are essential in mathematics for dealing with large numbers or repeated operations in a compact form, and they are used in many fields, such as algebra, calculus, and computer science.
Conclusion:
The exponential expression for 6 × 6 × 6 × 6 is 6⁴, which efficiently represents the repeated multiplication of 6 by itself four times.