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Solve for xx: 43x×46=14^{3x} \times 4^6 = 1

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Full solution

Q. Solve for xx: 43x×46=14^{3x} \times 4^6 = 1
  1. Combine Powers of 44: Combine the powers of 44 using the property of exponents: 4a+b=4a×4b4^{a+b} = 4^a \times 4^b.\newlineCalculation: 43x+6=14^{3x + 6} = 1
  2. Recognize Zero Power Rule: Recognize that any non-zero number raised to the power of 00 is 11.\newlineCalculation: 3x+6=03x + 6 = 0
  3. Solve for x: Solve for x by isolating x.\newlineCalculation: 3x=−63x = -6\newlinex=−6/3x = -6 / 3\newlinex=−2x = -2

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