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Which is equal to 147\frac{1}{4^7}?\newlineChoices:\newline(A) 1(4)7\frac{1}{(-4)^7}\newline(B) 1(4)7\frac{1}{(-4)^{-7}}\newline(C) 474^{-7}\newline(D) 47-4^7

Full solution

Q. Which is equal to 147\frac{1}{4^7}?\newlineChoices:\newline(A) 1(4)7\frac{1}{(-4)^7}\newline(B) 1(4)7\frac{1}{(-4)^{-7}}\newline(C) 474^{-7}\newline(D) 47-4^7
  1. Identify Base and Exponent: Identify the base and the exponent of 474^7. In 474^7, 44 is the base raised to the exponent 77. Base: 44 Exponent: 77
  2. Rewrite as Negative Exponent: Rewrite the expression 1/471 / 4^7 as a whole number with a negative exponent.\newlineMove 474^7 to the numerator and then make the exponent negative.\newline1/47=471 / 4^7 = 4^{-7}
  3. Choose Equivalent Expression: Choose the answer choice that is the equivalent expression for 1/471 / 4^7. 1/471 / 4^7 is equivalent to 474^{-7}, which is choice (C).