How do you write 100×10 in exponential form

How do you write 100×10 in exponential form?

The Correct Answer and Explanation is:

To express the product (100 \times 10) in exponential form, we start by breaking down each number into its prime factorization.

1. Understanding the Prime Factorization:

• The number (100) can be factored into primes as follows:
  [
  100 = 10 \times 10 = (10^1 \times 10^1) = 10^2
  ]
• The number (10) is already in its prime form, which is:
  [
  10 = 10^1
  ]

1. Combining the Expressions:

• Now, we can rewrite (100 \times 10) using the exponential forms we derived:
  [
  100 \times 10 = 10^2 \times 10^1
  ]

1. Applying the Exponential Rule:

• When multiplying numbers in exponential form that have the same base, we can use the rule of exponents:
  [
  a^m \times a^n = a^{m+n}
  ]
• Here, our base (a) is (10), and (m) and (n) correspond to the exponents (2) and (1), respectively:
  [
  10^2 \times 10^1 = 10^{2+1} = 10^3
  ]

1. Final Result:

• Therefore, the expression (100 \times 10) can be simplified in exponential form as:
  [
  100 \times 10 = 10^3
  ]

1. Understanding Exponential Notation:

• Exponential notation is a way of expressing numbers that are products of the same base multiplied by itself a certain number of times. In this case, (10^3) means (10) multiplied by itself three times:
  [
  10^3 = 10 \times 10 \times 10 = 1000
  ]
• This notation is not only useful for simplifying calculations but also for representing large numbers in a more compact form.

Thus, (100 \times 10) in exponential form is (10^3). This illustrates the efficiency and power of using exponents in mathematics, making it easier to handle calculations involving large numbers or repeated multiplications.