Apply Power Rule: We need to apply the power rule (a*b)^n = a^n * b^n to the expression (3xy^(4))^(3). Using the power rule, we get: (3xy^(4))^(3) = 3^(3) * (x)^(3) * (y^(4))^(3)Calculate 3^3: Now we calculate each part separately. First, we calculate 3^(3): 3^(3) = 3 * 3 * 3 = 27Calculate x^3: Next, we calculate (x)^(3): (x)^(3) = x * x * x = x^(3)Calculate y^12: Finally, we calculate (y^(4))^(3): Using the power of a power rule (a^(m))^n = a^(m*n), we get: (y^(4))^(3) = y^(4*3) = y^(12)Combine Final Expression: Now we combine all the parts together to get the final simplified expression: (3xy^(4))^(3) = 27 * x^(3) * y^(12)

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$\left(3 x y^{4}\right)^{3}$

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Math Problems

Algebra 1

Evaluate integers raised to rational exponents

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\left(3 x y^{4}\right)^{3}

Apply Power Rule: We need to apply the power rule $(a*b)^n = a^n * b^n$ to the expression $(3xy^{4})^{3}$ . Using the power rule, we get: $(3xy^{4})^{3} = 3^{3} * (x)^{3} * (y^{4})^{3}$
Calculate $3^3$ : Now we calculate each part separately. $\newline$ First, we calculate $3^{3}$ : $\newline$ $3^{3} = 3 \times 3 \times 3 = 27$
Calculate $x^3$ : Next, we calculate $(x)^{3}$ : $(x)^{3} = x \times x \times x = x^{3}$
Calculate $y^{12}$ : Finally, we calculate $(y^{4})^{3}$ : $\newline$ Using the power of a power rule $(a^{m})^{n} = a^{m*n}$ , we get: $\newline$ $(y^{4})^{3} = y^{4*3} = y^{12}$
Combine Final Expression: Now we combine all the parts together to get the final simplified expression: $\newline$ $(3xy^{4})^{3} = 27 \times x^{3} \times y^{12}$