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What is the value of A when we rewrite 4^(x+3)-4^(x) as A*4^(x)? A=◻

What is the value of AA when we rewrite 4x+3−4x4^{x+3}-4^{x} as A⋅4xA\cdot 4^{x} ?\newlineA=A= □\square

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Full solution

Q. What is the value of AA when we rewrite 4x+3−4x4^{x+3}-4^{x} as A⋅4xA\cdot 4^{x} ?\newlineA=A= □\square
  1. Factor out 4x4^{x}: First, factor out 4x4^{x} from the expression 4x+3−4x4^{x+3} - 4^{x}. \newline4x+3−4x=4x×(43−1)4^{x+3} - 4^{x} = 4^{x} \times (4^{3} - 1)
  2. Calculate 434^3: Calculate 434^3 and subtract 11. \newline43=644^3 = 64, so 43−1=64−1=634^3 - 1 = 64 - 1 = 63.
  3. Determine AA: Now, we have 4x×634^{x} \times 63, which means A=63A = 63.

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