Question

If a=2^m and b=2^m+1, show that 8a^3/b^2=2^m+1​

Answer 1

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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. (don't forget write at the end !!)

Hope it helps.

Answer 2

Answer:

Answer

Step-by-step explanation:

a^3=2^3m

=8a^3=2^3m+3

=b^2=2^2m+2

=8a^3/b^2=2^3m+3/2^2m+2

=in divide if base is equal the power subtract

=2^(3m+3)-(2m+2)

=2^3m+3-2m-2

=2^m+1

=2^m+1=2^m+1

=L.H.S =R.H.S(don't forget to write it)