Which expression is equivalent to 9^4 * 4^4? Choices: (A)36^8 (B)36^4 (C)1/36^4 (D)36^16

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Which expression is equivalent to 9^4 * 4^4?   Choices: (A)36^8 (B)36^4 (C)1/36^4 (D)36^16

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Identify Bases and Exponents: Identify the base numbers and their exponents in the given expression. The given expression is 9^4 * 4^4. Here, 9 and 4 are the bases, and both are raised to the power of 4.Factor Bases to Common Base: Factor the bases to express them as powers of a common base if possible. The number 9 can be written as 3^2, and the number 4 can be written as 2^2. Therefore, we can rewrite the expression as (3^2)^4 * (2^2)^4.Apply Power of Power Rule: Apply the power of a power rule, which states that (a^b)^c = a^(b*c). Using this rule, we get (3^2)^4 * (2^2)^4 = 3^(2*4) * 2^(2*4) = 3^8 * 2^8.Multiply Bases with Exponents: Multiply the expressions with the same exponents by combining the bases. Since both 3^8 and 2^8 have the same exponent, we can multiply the bases first and then apply the exponent. This gives us (3*2)^8 = 6^8.Factor 6 and Simplify: Recognize that 6^8 is not one of the answer choices, but 6 can be factored further. The number 6 can be written as 2*3, and since we already have 2^8 and 3^8 from the previous step, we can combine them to get (2*3)^8 = 6^8.Express in Terms of Base^4: Realize that 6^8 is not in the simplest form for comparison with the answer choices. We need to express 6^8 in terms of a base raised to the power of 4 to match the answer choices. Since 6 is 2*3, we can write 6^8 as (2^4 * 3^4)^2.Apply Distributive Property: Apply the distributive property of exponents over multiplication. We have (2^4 * 3^4)^2, which can be written as (2^4)^2 * (3^4)^2. This simplifies to 2^8 * 3^8, which is the same as 6^8 from the previous steps.Recognize Equivalent Expression: Recognize that 2^8 * 3^8 is equivalent to (2*3)^8, which is 6^8. We have already established that 6^8 is the simplified form of the given expression. Now we need to express it in terms of a base raised to the power of 4 to match the answer choices.Express in Terms of Base^4: Express 6^8 in terms of a base raised to the power of 4. Since 6^8 = (6^2)^4, and 6^2 is 36, we can write 6^8 as 36^4.Match to Answer Choices: Match the simplified expression to the answer choices. The expression 36^4 corresponds to choice (B) 36^4.

Which expression is equivalent to $9^4 \times 4^4$ ? $\newline$ Choices: $\newline$ (A) $36^8$ $\newline$ (B) $36^4$ $\newline$ (C) $1/36^4$ $\newline$ (D) $36^{16}$

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Which expression is equivalent to 94×449^4 \times 4^494×44?\newlineChoices:\newline(A) 36836^8368\newline(B) 36436^4364\newline(C) 1/3641/36^41/364\newline(D) 361636^{16}3616

Which expression is equivalent to $9^4 \times 4^4$ ? $\newline$ Choices: $\newline$ (A) $36^8$ $\newline$ (B) $36^4$ $\newline$ (C) $1/36^4$ $\newline$ (D) $36^{16}$