Question

If $(2^m)^4 =4^{6}$, find the value of m.

Answer 1

${(2} {}^{m} )^{4} = {4}^{6} \\ \\ = > {(2})^{4m} = {(2 {}^{2} })^{6} \\ \\ = > {(2)}^{4m} = {(2)}^{12} \\ \\ = > 4m = 12 \\ \\ = > m = \frac{12}{4} \\ \\ = > m = 3$

Answer 2

Solution :

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We know the Exponential laws:

i ) ( a^m )ⁿ = a^mn

ii ) If a^m = a^n then m = n

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Now ,

( 2^m )⁴ = 4^6

=> 2^4m = ( 2² )^6

=> 2^4m = 2^12

=> 4m = 12

Divide each term by 4 , we get

=> 4m/4 = 12/4

=> m = 3

Therefore ,

m = 3

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