Which expression is equivalent to 4^3 * 9^3? Choices: (A)36^3 (B)1/36^3 (C)36^6 (D)36^9

Understand the problem: Understand the problem. We need to find an expression equivalent to the product of 4^3 and 9^3.Use property of exponents: Use the property of exponents for products with the same exponent. When multiplying powers with the same exponent but different bases, we can combine the bases and keep the exponent the same. (a^m)(b^m) = (ab)^mApply property to 4^3 * 9^3: Apply the property to 4^3 * 9^3. Combine the bases 4 and 9, and keep the exponent 3. 4^3 * 9^3 = (4*9)^3Calculate product of bases: Calculate the product of the bases. 4 * 9 = 36Write final expression: Write the final expression using the combined base and the exponent. (4*9)^3 = 36^3Match final expression: Match the final expression with the given choices. The expression 36^3 corresponds to choice (A) 36^3.

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Math Problems

Algebra 1

Identify equivalent exponential expressions II

Full solution

Q. Which expression is equivalent to

4^3 \times 9^3

\newline

Choices:

\newline

(A)

36^3

\newline

(B)

\frac{1}{36^3}

\newline

(C)

36^6

\newline

(D)

36^9

Understand the problem: Understand the problem. $\newline$ We need to find an expression equivalent to the product of $4^3$ and $9^3$ .
Use property of exponents: Use the property of exponents for products with the same exponent. When multiplying powers with the same exponent but different bases, we can combine the bases and keep the exponent the same. (a^m)(b^m) = (ab)^m
Apply property to \(4^3 \times 9^3: Apply the property to $4^3 \times 9^3$ . $\newline$ Combine the bases $4$ and $9$ , and keep the exponent $3$ . $\newline$ $4^3 \times 9^3 = (4\times9)^3$
Calculate product of bases: Calculate the product of the bases. $4 \times 9 = 36$
Write final expression: Write the final expression using the combined base and the exponent. $\newline$ $(4\times9)^3 = 36^3$
Match final expression: Match the final expression with the given choices. $\newline$ The expression $36^3$ corresponds to choice (A) $36^3$ .