Question

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Answer 1

(16)^2m (64)^4 / (256)^2 = (256)^3m

(16)^2m (64)^4 = (256)^3m × (256)^2

(16)^2m (64)^4 =(256)^3m+2

(16)^2m (64)^4 = (16)^6m+4 {16^2 =256}

(64)^4 =(16)^6m+4 / (16)^2m

(64)^4=(16)^(6m+4-2m)

(64)^4=(16)^4m+4

(4)^4×3=(4)^8m+8 {64=16×4=4^2 ×4=4^3}

comparing the exponents or powers when base is same

we get

8m+8=12

8m=4

m=1/2

I hope it helps

Answer 2

Answer:

take (256)^2 to the RHS (right side)

AT right side -

$=256^{2} * 256^{3m}\\= 256^{2+3m}\\= 4^{4*(2+3m)}\\= 4^{8+12m}$                   $m^a * m^b (identity)\\\\= m^{a+b}$                $(m^a)^b (identity)\\= m^{ab}$

At left side-

$=16^{2m} * 64^{4}\\= 4^ {2*(2m)} * 4^{3*(4)}\\= 4^{4m} * 4^{12}\\= 4^{4m+12}$                   $m^a * m^b (identity)\\\\= m^{a+b}$                 $(m^a)^b (identity)\\= m^{ab}$

       

NOW EQUATE LEFT SIDE TO RIGHT SIDE

$4^{8+12m} = 4^{4m+12}\\or 8+12m = 4m+12\\\\ 8-12=4m-12m\\ -4=-8m\\ 4=8m\\ m=1/2$

I HOPE IT IS CORRECT!