Question

6. If a= 2m and b= 2m+1, show that 8a3 = 2+1 62​

Answer 1

Answer:

Take the LHS of the equation and solve it.

take cube of a => a^3 = 2^3m, 8a^3 = 2^(3m+3)   {since 8= 2*2*2, and powers add when multiplied with the same base.

b^2 = 2^(2m + 2)

therefore, 8a^3/b^2 = 2^(3m+3)  / 2^(2m + 2)

                                = powers will subtract.

                                = 2^ (m+1)

since LHS= RHS, Hence proved.