Simplify: 5c(3c^(2))^(3) A. 45c^(6) B. 135c^(6) C. 45c^(7) D. 135c^(7)

Simplify Inside Parentheses: First, we need to simplify the expression inside the parentheses, which is (3c^(2))^(3). According to the power of a power rule, we multiply the exponents when raising a power to a power. Calculation: (3c^(2))^(3) = 3^(3) * (c^(2))^(3) = 27c^(2*3) = 27c^(6)Multiply by Coefficient: Now, we multiply the result by the coefficient outside the parentheses, which is 5c. Calculation: 5c * 27c^(6) = 5 * 27 * c^(1+6) = 135c^(7)Final Answer: We have simplified the expression and found that the correct answer is 135c^(7), which corresponds to option D.

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Simplify: $5c(3c^{2})^{3}$ $\newline$ A. $45c^{6}$ $\newline$ B. $135c^{6}$ $\newline$ C. $45c^{7}$ $\newline$ D. $135c^{7}$

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Q. Simplify:

5c(3c^{2})^{3}

\newline

45c^{6}

\newline

135c^{6}

\newline

45c^{7}

\newline

135c^{7}

Simplify Inside Parentheses: First, we need to simplify the expression inside the parentheses, which is $(3c^{2})^{3}$ . According to the power of a power rule, we multiply the exponents when raising a power to a power. $\newline$ Calculation: $(3c^{2})^{3} = 3^{3} \times (c^{2})^{3} = 27c^{2\times3} = 27c^{6}$
Multiply by Coefficient: Now, we multiply the result by the coefficient outside the parentheses, which is $5c$ . $\newline$ Calculation: $5c \times 27c^{6} = 5 \times 27 \times c^{1+6} = 135c^{7}$
Final Answer: We have simplified the expression and found that the correct answer is $135c^{7}$ , which corresponds to option D.