Question

the value of M and n respectively if 108 is equal to 2^m *33*5^n​

Answer 1

Step-by-step explanation:

the value of M and n respectively if 108 is equal to 2^m *33*5^n

Answer 2

Given: 108 is equal to $2^{m} * 3^{3} * 5^{n}$

To find: The value of m and n.

Solution:

• The equation given in the question is as follows,

        $2^{m} * 3^{3} * 5^{n} = 108$

• In order to find the values of m and n, the H.C.F. (highest commom factor) of 108 must be calculated.
• On doing so, 108 can be equated to its factors as follows,

        $3^{3} * 2^{2} = 108$

• On comparing the two equations, it is found that 2 is to the power of 2, and hence it is concluded that m is 2.
• Since the factors of 108 do not consist of 5, the value of n is 0. This makes the value of $5^{n}$ equal to 1.

Therefore, the value of m and n is 2 and 0, respectively.