Select the equivalent expression. (3^(3)*6^(6))^(-3)=? Choose 1 answer: (A) (1)/(3^(9)*6^(18)) (B) (6^(18))/(3^(9)) (c) (3^(9))/(6^(18))

Question

Select the equivalent expression.  (3^(3)*6^(6))^(-3)=? Choose 1 answer: (A)  (1)/(3^(9)*6^(18)) (B)  (6^(18))/(3^(9)) (c)  (3^(9))/(6^(18))

Bytelearn · Accepted Answer

Understand Problem: Understand the problem and apply the power of a product rule. The problem asks us to find an equivalent expression for (3^(3)*6^(6))^(-3). According to the power of a product rule, (ab)^n = a^n * b^n, we can apply the negative exponent to both terms inside the parentheses.Apply Product Rule: Apply the negative exponent to both 3^3 and 6^6. (3^(3)*6^(6))^(-3) = (3^3)^(-3) * (6^6)^(-3)Apply Negative Exponent: Simplify the expression using the power of a power rule. According to the power of a power rule, (a^m)^n = a^(m*n), we multiply the exponents. (3^3)^(-3) * (6^6)^(-3) = 3^(3*(-3)) * 6^(6*(-3))Simplify Expression: Perform the multiplication of the exponents. 3^(3*(-3)) * 6^(6*(-3)) = 3^(-9) * 6^(-18)Perform Exponent Multiplication: Convert the negative exponents to positive exponents by taking the reciprocal. According to the negative exponent rule, a^(-n) = 1/a^n, we can rewrite the expression with positive exponents in the denominator. 3^(-9) * 6^(-18) = 1/(3^9) * 1/(6^18)Convert Negative Exponents: Combine the fractions. Since we are multiplying fractions, we multiply the numerators and the denominators separately. 1/(3^9) * 1/(6^18) = 1/(3^9 * 6^18)Combine Fractions: Identify the correct answer from the given options. The expression we have found is 1/(3^9 * 6^18), which matches option (A).

Select the equivalent expression. $\newline$ $(3^{3}\cdot6^{6})^{-3}=$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{1}{3^{9}\cdot6^{18}}$ $\newline$ (B) $\frac{6^{18}}{3^{9}}$ $\newline$ (C) $\frac{3^{9}}{6^{18}}$

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Select the equivalent expression.\newline(33⋅66)−3=(3^{3}\cdot6^{6})^{-3}=(33⋅66)−3=?\newlineChoose 111 answer:\newline(A) 139⋅618\frac{1}{3^{9}\cdot6^{18}}39⋅6181​\newline(B) 61839\frac{6^{18}}{3^{9}}39618​\newline(C) 39618\frac{3^{9}}{6^{18}}61839​

Select the equivalent expression. $\newline$ $(3^{3}\cdot6^{6})^{-3}=$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{1}{3^{9}\cdot6^{18}}$ $\newline$ (B) $\frac{6^{18}}{3^{9}}$ $\newline$ (C) $\frac{3^{9}}{6^{18}}$