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

Step-by-step explanation:

Solving in steps

Using exponent rules: a^b·a^c = a^(b+c) and (a^b)^c = a^(bc)

Step-by-step explanation:

the expression 4^−6⋅ 4^4⋅ (2^3⋅ 2^−4)^−1 can be solved using exponential rule:

= 4⁻⁶ * 4⁴ * (2³ * 2⁻⁴)⁻¹

= 4⁽⁻⁶ ⁺ ⁴⁾ * (2 ⁽³ ⁻ ⁴⁾ ) ⁻¹

= 4⁻² * (2⁻¹)⁻¹

= (2²) ⁻² * 2 ⁽⁻¹ ˣ ⁻¹⁾

= 2⁻⁴ * 2¹

= 2 ⁽⁻⁴ ⁺ ¹⁾

= 2 ⁻³

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