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Select all the expressions that are equivalent to 59×555^{-9} \times 5^{-5}. \newlineMulti-select Choices:\newline(A) 1545\frac{1}{5^{45}}\newline(B) 1514\frac{1}{5^{14}}\newline(C) 1514\frac{1}{5^{-14}}\newline(D) 5145^{-14}

Full solution

Q. Select all the expressions that are equivalent to 59×555^{-9} \times 5^{-5}. \newlineMulti-select Choices:\newline(A) 1545\frac{1}{5^{45}}\newline(B) 1514\frac{1}{5^{14}}\newline(C) 1514\frac{1}{5^{-14}}\newline(D) 5145^{-14}
  1. Combine exponents of base: Step 11: Combine the exponents of the same base.\newline59×55=5(9+5)=5145^{-9} \times 5^{-5} = 5^{(-9 + -5)} = 5^{-14}
  2. Convert negative exponent: Step 22: Convert the negative exponent to a positive exponent in the denominator. \newline514=15145^{-14} = \frac{1}{5^{14}}
  3. Compare with choices: Step 33: Compare the result with the given choices.\newline1514\frac{1}{5^{14}} matches choice (B)

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