Which expression is equivalent to 4^6 * 9^6? Choices: (A)36^12 (B)36^36 (C)36^6 (D)1/36^6

Question

Which expression is equivalent to 4^6 * 9^6?   Choices: (A)36^12 (B)36^36 (C)36^6 (D)1/36^6

Bytelearn · Accepted Answer

Identify Bases and Exponents: Identify the base and the exponents in the given expression. The given expression is 4^6 * 9^6. Here, 4 and 9 are the bases, and both are raised to the exponent 6.Recognize Perfect Squares: Recognize that 4 and 9 are perfect squares. 4 is the square of 2 (since 2^2 = 4), and 9 is the square of 3 (since 3^2 = 9). This can be rewritten as (2^2)^6 * (3^2)^6.Apply Power of Power Rule: Apply the power of a power rule. According to the power of a power rule, (a^b)^c = a^(b*c). Therefore, (2^2)^6 becomes 2^(2*6) and (3^2)^6 becomes 3^(2*6).Calculate New Exponents: Calculate the new exponents. 2^(2*6) = 2^12 and 3^(2*6) = 3^12. So the expression now is 2^12 * 3^12.Combine Bases with Multiplication: Combine the bases using multiplication. Since both bases are raised to the same exponent, we can multiply the bases together and keep the common exponent. This gives us (2*3)^12.Calculate Base Multiplication: Calculate the base multiplication. 2*3 equals 6. So the expression now is 6^12.Recognize Product of 4 and 9: Recognize that 6 is the product of 4 and 9. Since 4*9 equals 36, and we have 6^12, we can rewrite this as 36^6.Choose Equivalent Expression: Choose the equivalent expression for 4^6 * 9^6. The equivalent expression is 36^6, which corresponds to choice (C).

Which expression is equivalent to $4^6 \times 9^6$ ? $\newline$ Choices: $\newline$ (A) $36^{12}$ $\newline$ (B) $36^{36}$ $\newline$ (C) $36^6$ $\newline$ (D) $1/36^6$

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Which expression is equivalent to $4^6 \times 9^6$ ? $\newline$ Choices: $\newline$ (A) $36^{12}$ $\newline$ (B) $36^{36}$ $\newline$ (C) $36^6$ $\newline$ (D) $1/36^6$