Which expression is equivalent to 3^6 * 6^6? Choices: (A)1/18^6 (B)18^12 (C)18^6 (D)18^36

Question

Which expression is equivalent to 3^6 * 6^6?   Choices: (A)1/18^6 (B)18^12 (C)18^6 (D)18^36

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Identify Bases and Exponents: Identify the bases and the exponents in the expression 3^6 * 6^6. We have two terms, 3^6 and 6^6, with bases 3 and 6, and both raised to the exponent 6.Prime Factors of 6: Recognize that 6 can be written as a product of its prime factors. The number 6 is equal to 2 * 3. Therefore, 6^6 can be rewritten as (2 * 3)^6.Power of a Product Rule: Apply the power of a product rule to (2 * 3)^6. According to the power of a product rule, (ab)^n = a^n * b^n. So, (2 * 3)^6 = 2^6 * 3^6.Substitute and Combine Terms: Substitute 6^6 with 2^6 * 3^6 in the original expression. Now we have 3^6 * 6^6 = 3^6 * (2^6 * 3^6).Combine Like Terms: Combine like terms by adding the exponents of the same base. We have two terms with the base 3, so we add their exponents: 3^6 * 3^6 = 3^(6+6) = 3^12.Multiply Remaining Terms: Multiply the remaining terms. Now we have 3^12 * 2^6. Since these terms do not have the same base, we cannot combine them further.Power of a Power Rule: Recognize that 3^12 can be written as (3^6)^2. Using the power of a power rule, (a^n)^m = a^(n*m), we have (3^6)^2 = 3^(6*2) = 3^12.Combine Expressions: Combine the expressions (3^6)^2 and 2^6. Now we have (3^6)^2 * 2^6 = 3^12 * 2^6.Rearrange Terms: Recognize that 3^12 * 2^6 can be written as (3^6 * 2^6) * 3^6. We can rearrange the terms to group them as (3^6 * 2^6) * 3^6.Substitute Back Expression: Substitute back the expression for 6^6. We know that 6^6 = 2^6 * 3^6, so we can write (3^6 * 2^6) * 3^6 as 6^6 * 3^6.Full Circle to Original: Recognize that we have come full circle to the original expression. We have shown that 3^6 * 6^6 = 6^6 * 3^6, which is the same as the original expression.Simplify the Expression: Simplify the expression 6^6 * 3^6. Since 6^6 = (2 * 3)^6, we can write 6^6 * 3^6 as (2 * 3)^6 * 3^6 = 2^6 * 3^12.Correct Mistake: Recognize that we have made a mistake in the previous steps. We have incorrectly circled back to the original expression without simplifying it correctly. We need to correct this mistake.

Which expression is equivalent to $3^6 \times 6^6$ ? $\newline$ Choices: $\newline$ (A) $\frac{1}{18^6}$ $\newline$ (B) $18^{12}$ $\newline$ (C) $18^6$ $\newline$ (D) $18^{36}$

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Which expression is equivalent to 36×663^6 \times 6^636×66?\newlineChoices:\newline(A) 1186\frac{1}{18^6}1861​\newline(B) 181218^{12}1812\newline(C) 18618^6186\newline(D) 183618^{36}1836

Which expression is equivalent to $3^6 \times 6^6$ ? $\newline$ Choices: $\newline$ (A) $\frac{1}{18^6}$ $\newline$ (B) $18^{12}$ $\newline$ (C) $18^6$ $\newline$ (D) $18^{36}$