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The expression 
(x^(-12))(x^(4)) is equivalent to 
x^(k). What is the value of 
k ?
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The expression (x12)(x4) \left(x^{-12}\right)\left(x^{4}\right) is equivalent to xk x^{k} . What is the value of k k ?\newline

Full solution

Q. The expression (x12)(x4) \left(x^{-12}\right)\left(x^{4}\right) is equivalent to xk x^{k} . What is the value of k k ?\newline
  1. Identify Exponents: We are given the expression x(12)×x(4)x^{(-12)} \times x^{(4)} and we need to find the equivalent expression in the form of x(k)x^{(k)}. According to the laws of exponents, when we multiply two expressions with the same base, we add their exponents.\newlineCalculation: k=(12)+(4)k = (-12) + (4)
  2. Calculate Value of k: Perform the addition to find the value of k.\newlineCalculation: k=12+4=8k = -12 + 4 = -8
  3. Find Equivalent Expression: We have found the value of kk to be 8-8. This means that the expression x(12)×x(4)x^{(-12)} \times x^{(4)} is equivalent to x(8)x^{(-8)}.