Question

Express$16,200$ as a product of powers of prime numbers.

• A. $2^3\times 3^3\times 5^4$
• B. $2^3\times 3^3\times 5^3$
• C. $2^4\times 3^3\times 5^3$
• D. $2^3\times 3^4\times 5^2$

Answer 1

The correct option is D $2^3\times 3^4\times 5^2$

$16200=2\times 8100$

$=2\times 2\times 4050$

$=2\times 2\times 2\times 2025$

$=2\times 2\times 2\times 5\times 405$

$=2\times 2\times 2\times 5\times 5\times 81$

$=2\times 2\times 2\times 5\times 5\times 3\times 27$

$=2\times 2\times 2\times 5\times 5\times 3\times 3\times 9$

$=2\times 2\times 2\times 5\times 5\times 3\times 3\times 3\times 3$

$=2^3\times 5^2\times 3^4$