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(−2)2n=16(-2)^{2n} = 16

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Full solution

Q. (−2)2n=16(-2)^{2n} = 16
  1. Understand Equation and Goal: Understand the equation and the goal.\newlineWe need to find the value of nn such that (−2)(-2) raised to the power of 2n2n equals 1616.\newline(−2)2n=16(-2)^{2n} = 16
  2. Simplify the Equation: Simplify the equation.\newlineSince (−2)2n(-2)^{2n} can be written as [(−2)2]n[(-2)^2]^n and (−2)2(-2)^2 is 44, we can rewrite the equation as:\newline4n=164^n = 16
  3. Recognize Power of 44: Recognize that 1616 is a power of 44. 1616 is 44 squared, which means 1616 can be written as 424^2. So, we can set the exponents equal to each other since the bases are the same. n=2n = 2

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