Question

2ⁿ×5m=200 fine the value of m and n

Answer 1

Question

2ⁿ×5ᵐ=200

Explanation

After the prime factorization of 200,

we have $\sf{200=2^3\times5^2}$

Compare it to 2ⁿ×5ᵐ=200

Therefore we get n=3 and m=2.

For more information, see below.

Prime Factorization of 200

200 is divisible by 10, after the division

$\sf{200=2\times10^2}$

$\sf{200=2\times(2\times5)^2 \to [10=2\times5]}$

$\sf{200=2\times2^2\times5^2}$

∴$\sf{200=2^3\times5^2}$

Extra Explanation

• Uniqueness

The prime factorization is unique. Here we have a multiplication of primes 2 and 5. Which is unique, so no other factorizations can correspond to 200.

• Base and Exponent

In 2ⁿ, 2 is called the base. n is called the exponent.