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Which of the following is equivalent to (2x^(3)y^(4)z^(5))^(3) ? Choose 1 answer: (A) 6x^(9)y^(12)z^(15) (B) 8x^(9)y^(12)z^(15) (C) 6x^(6)y^(7)z^(8) (D) 8x^(6)y^(7)z^(8)

Which of the following is equivalent to (2x3y4z5)3 \left(2 x^{3} y^{4} z^{5}\right)^{3} ?\newlineChoose 11 answer:\newline(A) 6x9y12z15 6 x^{9} y^{12} z^{15} \newline(B) 8x9y12z15 8 x^{9} y^{12} z^{15} \newline(C) 6x6y7z8 6 x^{6} y^{7} z^{8} \newline(D) 8x6y7z8 8 x^{6} y^{7} z^{8}

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Full solution

Q. Which of the following is equivalent to (2x3y4z5)3 \left(2 x^{3} y^{4} z^{5}\right)^{3} ?\newlineChoose 11 answer:\newline(A) 6x9y12z15 6 x^{9} y^{12} z^{15} \newline(B) 8x9y12z15 8 x^{9} y^{12} z^{15} \newline(C) 6x6y7z8 6 x^{6} y^{7} z^{8} \newline(D) 8x6y7z8 8 x^{6} y^{7} z^{8}
  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 each term inside the parentheses.\newline(2x3y4z5)3=23×(x3)3×(y4)3×(z5)3(2x^{3}y^{4}z^{5})^{3} = 2^{3} \times (x^{3})^{3} \times (y^{4})^{3} \times (z^{5})^{3}
  2. Calculate powers: Calculate the powers.\newlineNow we calculate each term separately:\newline23=2×2×2=82^{3} = 2 \times 2 \times 2 = 8\newline(x3)3=x3×3=x9(x^{3})^{3} = x^{3\times3} = x^{9}\newline(y4)3=y4×3=y12(y^{4})^{3} = y^{4\times3} = y^{12}\newline(z5)3=z5×3=z15(z^{5})^{3} = z^{5\times3} = z^{15}
  3. Combine the results: Combine the results.\newlineCombining the results from Step 22, we get:\newline8⋅x9⋅y12⋅z158 \cdot x^{9} \cdot y^{12} \cdot z^{15}
  4. Match with given options: Match the result with the given options.\newlineThe result from Step 33 matches option (B):\newline(B) 8x9y12z158x^{9}y^{12}z^{15}

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