for question one it says to write it in exponential notation: 13x13x13.
for question two its says to write it in exponential notation: 8x8x8x8x8x8.
for question three its says to write it in exponential notation: 64×64.
for question four its says to write it in exponential notation: 4x4x4x4x4x4x4x4.
The Correct Answer and Explanation is:
Sure! Let’s go through each question carefully, provide the correct exponential notation, and then I’ll give a detailed explanation.
Question 1:
Write in exponential notation:
13 × 13 × 13
Answer:
13313^3
Question 2:
Write in exponential notation:
8 × 8 × 8 × 8 × 8 × 8
Answer:
868^6
Question 3:
Write in exponential notation:
64 × 64
Answer:
64264^2
Question 4:
Write in exponential notation:
4 × 4 × 4 × 4 × 4 × 4 × 4 × 4
Answer:
484^8
Detailed Explanation (300+ words):
Exponential notation is a way of expressing repeated multiplication of the same number in a compact form. Instead of writing the number multiplied by itself multiple times, exponential notation uses a base and an exponent (also called the power).
- The base is the number that is multiplied repeatedly.
- The exponent tells how many times the base is multiplied by itself.
For example, ana^n means the base aa is multiplied by itself nn times.
Let’s apply this idea to your questions:
Question 1: 13 × 13 × 13
Here, the base is 13, and since 13 is multiplied by itself 3 times, the exponent is 3. So, it is written as 13313^3.
Question 2: 8 × 8 × 8 × 8 × 8 × 8
The base is 8, and it appears 6 times in multiplication. So, in exponential form, it’s 868^6.
Question 3: 64 × 64
Two 64s multiplied together means the base is 64 and the exponent is 2, giving 64264^2.
Question 4: 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4
The base is 4, and since it is multiplied by itself 8 times, the exponential notation is 484^8.
Why use exponential notation?
- Simplifies writing: Instead of writing long multiplication, exponentials make it easy to write and understand the number of times a number is multiplied.
- Makes calculations easier: Many mathematical operations and formulas become more manageable with exponential notation.
- Foundation for advanced math: Exponents are used in algebra, calculus, science, and many real-life applications like calculating compound interest or growth rates.
In summary, exponential notation expresses repeated multiplication succinctly with a base and an exponent, where the exponent indicates the number of times the base is multiplied by itself. This helps in simplifying mathematical expressions and is a fundamental concept in mathematics.