Select the equivalent expression 6*6*6*6*6 find 2 answers (A) (6^2)^3 (B) 2^5 * 3^5 (C) 6^6/6^1 (D) 3^2 * 2^3

Understand the problem: Understand the problem. We need to find which expressions are equivalent to multiplying 6 by itself 5 times, which is written as 6*6*6*6*6.Evaluate options: Evaluate each option to see if it is equivalent to 6*6*6*6*6. Starting with option (A) (6^2)^3, we need to determine if this expression is equivalent to 6 raised to the 5th power. (6^2)^3 = 6^(2*3) = 6^6, which is not the same as 6^5.Check option (A): Move on to option (B) 2^5 * 3^5. We need to check if multiplying 2^5 by 3^5 is equivalent to 6^5. 2^5 * 3^5 = (2*3)^5 = 6^5, which is the same as 6*6*6*6*6.Check option (B): Evaluate option (C) 6^6/6^1. We need to simplify this expression to see if it equals 6^5. 6^6/6^1 = 6^(6-1) = 6^5, which is equivalent to 6*6*6*6*6.Check option (C): Finally, look at option (D) 3^2 * 2^3. We need to determine if this expression equals 6^5. 3^2 * 2^3 = (3*3) * (2*2*2) = 9 * 8, which is not the same as 6^5.

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Select the equivalent expression $6\times 6\times 6\times 6\times 6$ $\newline$ find $2$ answers $\newline$ (A) $(6^2)^3$ $\newline$ (B) $2^5 \cdot 3^5$ $\newline$ (C) $\frac{6^6}{6^1}$ $\newline$ (D) $3^2 \cdot 2^3$

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Precalculus

Partial sums of geometric series

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Q. Select the equivalent expression

6\times 6\times 6\times 6\times 6

\newline

find

2

answers

\newline

(A)

(6^2)^3

\newline

(B)

2^5 \cdot 3^5

\newline

(C)

\frac{6^6}{6^1}

\newline

(D)

3^2 \cdot 2^3

Understand the problem: Understand the problem. $\newline$ We need to find which expressions are equivalent to multiplying $6$ by itself $5$ times, which is written as $6 \times 6 \times 6 \times 6 \times 6$ .
Evaluate options: Evaluate each option to see if it is equivalent to $6\times6\times6\times6\times6$ . Starting with option (A) $(6^2)^3$ , we need to determine if this expression is equivalent to $6$ raised to the $5$ th power. $(6^2)^3 = 6^{(2\times3)} = 6^6$ , which is not the same as $6^5$ .
Check option (A): Move on to option (B) $2^5 \times 3^5$ . We need to check if multiplying $2^5$ by $3^5$ is equivalent to $6^5$ . $2^5 \times 3^5 = (2\times3)^5 = 6^5$ , which is the same as $6\times6\times6\times6\times6$ .
Check option (B): Evaluate option (C) $6^6/6^1$ . We need to simplify this expression to see if it equals $6^5$ . $6^6/6^1 = 6^{(6-1)} = 6^5$ , which is equivalent to $6*6*6*6*6$ .
Check option (C): Finally, look at option (D) $3^2 \times 2^3$ . We need to determine if this expression equals $6^5$ . $3^2 \times 2^3 = (3\times3) \times (2\times2\times2) = 9 \times 8$ , which is not the same as $6^5$ .