Write each of the following expressions as a power of 2: 4^−6⋅ 4^4⋅ (2^3⋅ 2^−4)^−1

Answer 1

Apply​ exponent rule:

( a^b )^c = a^bc

4 = 2^2

4^( - 6 ) = ( 2^2 )^( - 6 ) = 2^( - 12 )

4^4 = ( 2^2 )^4 = 2^8

2^3 ∙ 2^( - 4 ) = 2^( - 1 )

( 2^3 ∙ 2^( - 4 ) ) ^( - 1) = ( 2^( - 1 ) )^( - 1 ) = 2^1 = 2

4^( - 6 ) ∙ 4^4 ∙ 2^3 ∙ 2^( - 4 ) ) ^( - 1) = 2^( - 12 ) ∙ 2^8 ∙ 2^1 = 2^( - 3 )

Answer 2

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