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Simplifique la siguiente expresión exponencial. 3*2^(x+1)-4*2^(x).

Simplifique la siguiente expresión exponencial. 3⋅2x+1−4⋅2x 3 \cdot 2^{x+1}-4 \cdot 2^{x} .

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Full solution

Q. Simplifique la siguiente expresión exponencial. 3⋅2x+1−4⋅2x 3 \cdot 2^{x+1}-4 \cdot 2^{x} .
  1. Factor out common term: Factor out the common term 2x2^x.
    3imes2x+1−4imes2x3 imes 2^{x+1} - 4 imes 2^x
    =3imes2ximes2−4imes2x= 3 imes 2^x imes 2 - 4 imes 2^x
  2. Combine like terms: Simplify the expression by combining like terms.
    =2x⋅(3⋅2−4) = 2^x \cdot (3 \cdot 2 - 4)
    =2x⋅(6−4) = 2^x \cdot (6 - 4)
  3. Perform subtraction: Perform the subtraction inside the parentheses.
    =2x⋅(2)= 2^x \cdot (2)
    =2⋅2x= 2 \cdot 2^x
  4. Simplify final expression: Simplify the final expression. =2(x+1)= 2^{(x+1)}

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