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Fully simplify. (4x^(2)y^(5))^(3) Answer:

Fully simplify.\newline(4x2y5)3 \left(4 x^{2} y^{5}\right)^{3} \newlineAnswer:

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Full solution

Q. Fully simplify.\newline(4x2y5)3 \left(4 x^{2} y^{5}\right)^{3} \newlineAnswer:
  1. Apply Power Rule: Apply the power of a power rule, which states that (am)n=am∗n(a^{m})^{n} = a^{m*n}, to the given expression (4x2y5)3(4x^{2}y^{5})^{3}.(4x2y5)3=43×(x2)3×(y5)3(4x^{2}y^{5})^{3} = 4^{3} \times (x^{2})^{3} \times (y^{5})^{3}
  2. Calculate Powers: Calculate the powers for each component of the expression.\newline43=4×4×4=644^{3} = 4 \times 4 \times 4 = 64\newline(x2)3=x2×3=x6(x^{2})^{3} = x^{2\times3} = x^{6}\newline(y5)3=y5×3=y15(y^{5})^{3} = y^{5\times3} = y^{15}
  3. Combine Results: Combine the results from Step 22 to get the final simplified expression.\newline(4x2y5)3=64x6y15(4x^{2}y^{5})^{3} = 64x^{6}y^{15}

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