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(2b^(-5))^(3) Which of the following is equivalent to the given expression for all b!=0 ? Choose 1 answer: (A) (2)/(b^(15)) (B) (8)/(b^(15)) (c) (1)/(2b^(15)) (D) (1)/(8b^(15))

(2b−5)3 \left(2 b^{-5}\right)^{3} \newlineWhich of the following is equivalent to the given expression for all b≠0 b \neq 0 ?\newlineChoose 11 answer:\newline(A) 2b15 \frac{2}{b^{15}} \newline(B) 8b15 \frac{8}{b^{15}} \newline(C) 12b15 \frac{1}{2 b^{15}} \newline(D) 18b15 \frac{1}{8 b^{15}}

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Q. (2b−5)3 \left(2 b^{-5}\right)^{3} \newlineWhich of the following is equivalent to the given expression for all b≠0 b \neq 0 ?\newlineChoose 11 answer:\newline(A) 2b15 \frac{2}{b^{15}} \newline(B) 8b15 \frac{8}{b^{15}} \newline(C) 12b15 \frac{1}{2 b^{15}} \newline(D) 18b15 \frac{1}{8 b^{15}}
  1. Apply power of power rule: Apply the power of a power rule.\newlineThe power of a power rule states that (am)n=am∗n(a^m)^n = a^{m*n}. We will apply this rule to the given expression (2b−5)3(2b^{-5})^3.\newline(2b−5)3=23⋅(b−5)3(2b^{-5})^3 = 2^3 \cdot (b^{-5})^3
  2. Calculate powers: Calculate the powers.\newlineNow we calculate the powers separately for 232^3 and (b−5)3(b^{-5})^3.\newline23=2×2×2=82^3 = 2 \times 2 \times 2 = 8\newline(b−5)3=b−5×3=b−15(b^{-5})^3 = b^{-5 \times 3} = b^{-15}
  3. Combine results: Combine the results.\newlineWe combine the results from Step 22 to get the final expression.\newline(2b−5)3=8⋅b−15(2b^{-5})^3 = 8 \cdot b^{-15}
  4. Write expression with positive exponent: Write the expression with positive exponent.\newlineSince b−15b^{-15} means 1/(b15)1/(b^{15}), we rewrite the expression with a positive exponent.\newline8⋅b−15=8/(b15)8 \cdot b^{-15} = 8 / (b^{15})
  5. Match result with given choices: Match the result with the given choices.\newlineThe expression we found is 8b15\frac{8}{b^{15}}, which matches choice (B).

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