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Fully simplify. (6x^(5)y^(2))^(3) Answer:

Fully simplify.\newline(6x5y2)3 \left(6 x^{5} y^{2}\right)^{3} \newlineAnswer:

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Full solution

Q. Fully simplify.\newline(6x5y2)3 \left(6 x^{5} y^{2}\right)^{3} \newlineAnswer:
  1. Apply Power Rule: Apply the power of a power rule to the expression.\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 part of the expression (6x5y2)3(6x^{5}y^{2})^{3}.
  2. Apply Rule to Coefficient: Apply the rule to the numerical coefficient.\newline(63)=6×6×6=216(6^{3}) = 6\times6\times6 = 216.
  3. Apply Rule to xx Variable: Apply the rule to the xx variable.(x5)3=x5⋅3=x15.(x^{5})^{3} = x^{5\cdot3} = x^{15}.
  4. Apply Rule to yy Variable: Apply the rule to the yy variable.(y2)3=y2⋅3=y6\left(y^{2}\right)^{3} = y^{2\cdot3} = y^{6}.
  5. Combine Results: Combine the results from steps 22, 33, and 44. The fully simplified expression is 216x15y6216x^{15}y^{6}.

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