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(2y^(2)z^(10))^(5) Which of the following expressions is equivalent to the given expression? Choose 1 answer: (A) 10y^(32)z^(100,000) (B) 10y^(10)z^(50) (C) 32y^(32)z^(100,000) (D) 32y^(10)z^(50)

(2y2z10)5 \left(2 y^{2} z^{10}\right)^{5} \newlineWhich of the following expressions is equivalent to the given expression?\newlineChoose 11 answer:\newline(A) 10y32z100,000 10 y^{32} z^{100,000} \newline(B) 10y10z50 10 y^{10} z^{50} \newline(C) 32y32z100,000 32 y^{32} z^{100,000} \newline(D) 32y10z50 32 y^{10} z^{50}

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Full solution

Q. (2y2z10)5 \left(2 y^{2} z^{10}\right)^{5} \newlineWhich of the following expressions is equivalent to the given expression?\newlineChoose 11 answer:\newline(A) 10y32z100,000 10 y^{32} z^{100,000} \newline(B) 10y10z50 10 y^{10} z^{50} \newline(C) 32y32z100,000 32 y^{32} z^{100,000} \newline(D) 32y10z50 32 y^{10} z^{50}
  1. Apply power of power rule: Apply the power of a power rule to the given expression.\newlineThe power of a power rule states that (am)n=am∗n(a^{m})^{n} = a^{m*n}. We apply this rule to each part of the expression separately.\newline(2y2z10)5=25⋅(y2)5⋅(z10)5(2y^{2}z^{10})^{5} = 2^{5} \cdot (y^{2})^{5} \cdot (z^{10})^{5}
  2. Calculate each part: Calculate each part of the expression using the power of a power rule.\newline25=322^{5} = 32\newline(y2)5=y2⋅5=y10(y^{2})^{5} = y^{2\cdot5} = y^{10}\newline(z10)5=z10⋅5=z50(z^{10})^{5} = z^{10\cdot5} = z^{50}
  3. Combine the results: Combine the results to get the final expression.\newlineThe final expression is 32⋅y10⋅z5032 \cdot y^{10} \cdot z^{50}.
  4. Match with given choices: Match the final expression with the given choices.\newlineThe final expression 32⋅y10⋅z5032 \cdot y^{10} \cdot z^{50} matches with choice (D).

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