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

Evaluate Options: We need to find an expression that is equivalent to multiplying 6 by itself 5 times, which is written as 6^5. Let's evaluate each option to see which one is equivalent to 6^5.Option (A): Option (A) is (6^2)^3. Using the power of a power rule, which states that (a^m)^n = a^(m*n), we calculate (6^2)^3 as 6^(2*3) = 6^6. This is not equal to 6^5.Option (B): Option (B) is 2^5 * 3^5. Using the rule that (ab)^n = a^n * b^n, we can rewrite 6^5 as (2*3)^5, which is equal to 2^5 * 3^5. This option is equivalent to 6^5.Option (C): Option (C) is 6^6/6^1. Using the quotient of powers rule, which states that a^m / a^n = a^(m-n), we calculate 6^6/6^1 as 6^(6-1) = 6^5. This option is also equivalent to 6^5.Option (D): Option (D) is 3^2 * 2^3. This option is not equivalent to 6^5 because 3^2 * 2^3 = 9 * 8 = 72, which is not the same as 6 multiplied by itself 5 times.

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Select the equivalent expression $6\times 6\times 6\times 6\times 6$ $\newline$ (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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Math Problems

Grade 7

Add and subtract like terms: with exponents

Full solution

Q. Select the equivalent expression

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

\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

Evaluate Options: We need to find an expression that is equivalent to multiplying $6$ by itself $5$ times, which is written as $6^5$ . Let's evaluate each option to see which one is equivalent to $6^5$ .
Option (A): Option (A) is $(6^2)^3$ . Using the power of a power rule, which states that $(a^m)^n = a^{m*n}$ , we calculate $(6^2)^3$ as $6^{2*3} = 6^6$ . This is not equal to $6^5$ .
Option (B): Option (B) is $2^5 \times 3^5$ . Using the rule that $(ab)^n = a^n \times b^n$ , we can rewrite $6^5$ as $(2\times3)^5$ , which is equal to $2^5 \times 3^5$ . This option is equivalent to $6^5$ .
Option (C): Option (C) is $6^6/6^1$ . Using the quotient of powers rule, which states that $a^m / a^n = a^{(m-n)}$ , we calculate $6^6/6^1$ as $6^{(6-1)} = 6^5$ . This option is also equivalent to $6^5$ .
Option (D): Option (D) is $3^2 \times 2^3$ . This option is not equivalent to $6^5$ because $3^2 \times 2^3 = 9 \times 8 = 72$ , which is not the same as $6$ multiplied by itself $5$ times.