Prime factorisation of 10000
Understand the Problem
The question is asking for the prime factorization of the number 10000. This involves breaking down the number into its prime factors, which are the prime numbers that multiply together to result in 10000.
Answer
$2^4 \times 5^4$
Answer for screen readers
The prime factorization of 10000 is $2^4 \times 5^4$.
Steps to Solve
-
Start with the number 10000 To find the prime factorization of 10000, we can start by expressing it as a power of 10: $$ 10000 = 10^4 $$
-
Break down 10 into prime factors Next, we can factor 10 into its prime factors. The number 10 can be expressed as: $$ 10 = 2 \times 5 $$
-
Substitute prime factors into the power equation Now, substitute $10$ with its prime factors in the expression for 10000: $$ 10000 = (2 \times 5)^4 $$
-
Apply the power of a product property We now apply the property of exponents that states $(ab)^n = a^n \times b^n$: $$ 10000 = 2^4 \times 5^4 $$
-
Calculate the values of the powers Now we can calculate the powers: $$ 2^4 = 16 $$ $$ 5^4 = 625 $$
-
Combine the results to write the final factorization Thus, we have: $$ 10000 = 16 \times 625 $$ The complete prime factorization can thus be expressed as: $$ 10000 = 2^4 \times 5^4 $$
The prime factorization of 10000 is $2^4 \times 5^4$.
More Information
The prime factorization shows that 10000 is made up of the prime number 2 raised to the power of 4 and the prime number 5 raised to the power of 4. This indicates that multiplying these two factors together gives the original number. Prime factorization is a fundamental concept in number theory and is useful in many areas of mathematics.
Tips
- Forgetting to multiply the powers when using the exponent rules. Always ensure to apply the exponent rules correctly.
- Not recognizing a number can be expressed as a power, such as $10^4$ in this case. It's important to look for these representations.
