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))

Apply negative exponent rule: Apply the negative exponent rule. The negative exponent rule states that a^(-n) = 1/a^n. We will apply this rule to the entire expression. (3^(3)*6^(6))^(-3) = 1 / (3^(3)*6^(6))^(3)Apply power of product rule: Apply the power of a product rule. The power of a product rule states that (ab)^n = a^n * b^n. We will apply this rule to the expression inside the parentheses. 1 / (3^(3)*6^(6))^(3) = 1 / (3^(3))^3 * (6^(6))^3Simplify exponents: Simplify the exponents. When raising a power to a power, you multiply the exponents. We will do this for both terms. 1 / (3^(3))^3 * (6^(6))^3 = 1 / (3^(3*3)) * (6^(6*3))Calculate exponents: Calculate the exponents. Now we will calculate the exponents for both 3 and 6. 1 / (3^(3*3)) * (6^(6*3)) = 1 / (3^(9)) * (6^(18))Write final expression: Write the final expression. The final expression is the reciprocal of the product of 3 to the 9th power and 6 to the 18th power. 1 / (3^(9) * 6^(18))

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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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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. 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}}

Apply negative exponent rule: Apply the negative exponent rule. $\newline$ The negative exponent rule states that $a^{-n} = \frac{1}{a^n}$ . We will apply this rule to the entire expression. $\newline$ $(3^{3}*6^{6})^{-3} = \frac{1}{(3^{3}*6^{6})^{3}}$
Apply power of product rule: Apply the power of a product rule. $\newline$ The power of a product rule states that $(ab)^n = a^n \times b^n$ . We will apply this rule to the expression inside the parentheses. $\newline$ $\frac{1}{(3^{3}\times6^{6})^{3}} = \frac{1}{(3^{3})^3 \times (6^{6})^3}$
Simplify exponents: Simplify the exponents. $\newline$ When raising a power to a power, you multiply the exponents. We will do this for both terms. $\newline$ $\frac{1}{(3^{3})^{3}} \times (6^{6})^{3} = \frac{1}{3^{3\times3}} \times 6^{6\times3}$
Calculate exponents: Calculate the exponents. $\newline$ Now we will calculate the exponents for both $3$ and $6$ . $\newline$ $\frac{1}{(3^{3\times3})} \times (6^{6\times3}) = \frac{1}{(3^{9})} \times (6^{18})$
Write final expression: Write the final expression. $\newline$ The final expression is the reciprocal of the product of $3$ to the $9$ th power and $6$ to the $18$ th power. $\newline$ $1 / (3^{9} * 6^{18})$