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Select all the expressions that are equivalent to (83)1(8^{-3})^1.\newlineMulti-select Choices:\newline(A) 183\frac{1}{8^3}\newline(B) 183\frac{1}{8^{-3}}\newline(C) 828^{-2}\newline(D) 182\frac{1}{8^{-2}}

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Q. Select all the expressions that are equivalent to (83)1(8^{-3})^1.\newlineMulti-select Choices:\newline(A) 183\frac{1}{8^3}\newline(B) 183\frac{1}{8^{-3}}\newline(C) 828^{-2}\newline(D) 182\frac{1}{8^{-2}}
  1. Understand the expression: Understand the expression (83)1(8^{-3})^1.\newlineThe expression (83)1(8^{-3})^1 means that we have 88 raised to the power of 3-3, and then this result is raised to the power of 11. Raising any number to the power of 11 leaves the number unchanged.\newline(83)1=83(8^{-3})^1 = 8^{-3}
  2. Compare with given choices: Compare the expression 838^{-3} to the choices given.\newlineWe need to determine which of the given choices are equivalent to 838^{-3}.\newline(A) 183\frac{1}{8^3} is equivalent to 838^{-3} because a negative exponent indicates the reciprocal of the base raised to the positive exponent.\newline83=1838^{-3} = \frac{1}{8^3}

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