Which expressions are equivalent to $\newline$ $7^7\cdot7^7\cdot7^7$ ? $\newline$ Choose $2$ answers: $\newline$ (A) $\frac{7^8}{7^2}$ $\newline$ (B) $7^6\cdot7^1$ $\newline$ (C) $(7^2)^3$ $\newline$ (D) $\frac{7^{12}}{7^2}$

Full solution

Q. Which expressions are equivalent to

\newline

7^7\cdot7^7\cdot7^7

\newline

Choose

2

answers:

\newline

(A)

\frac{7^8}{7^2}

\newline

(B)

7^6\cdot7^1

\newline

(C)

(7^2)^3

\newline

(D)

\frac{7^{12}}{7^2}

Understand the original expression: Understand the original expression. $\newline$ The original expression is $7*7*7*7*7*7$ , which is $7$ raised to the power of $6$ , or $7^6$ .
Evaluate option A: Evaluate option A. $\newline$ Option A is $(7^8)/(7^2)$ . Using the rule of exponents for division, we subtract the exponents: $8 - 2 = 6$ . So, $(7^8)/(7^2)$ simplifies to $7^{(8-2)} = 7^6$ .
Evaluate option B: Evaluate option B. $\newline$ Option B is $7^6\times7^1$ . Using the rule of exponents for multiplication, we add the exponents: $6 + 1 = 7$ . So, $7^6\times7^1$ simplifies to $7^{6+1} = 7^7$ , which is not equivalent to $7^6$ .
Evaluate option C: Evaluate option C. $\newline$ Option C is $(7^2)^3$ . Using the rule of exponents for powers, we multiply the exponents: $2 \times 3 = 6$ . So, $(7^2)^3$ simplifies to $7^{2\times3} = 7^6$ .
Evaluate option D: Evaluate option D. $\newline$ Option D is $(7^{12})/(7^2)$ . Using the rule of exponents for division, we subtract the exponents: $12 - 2 = 10$ . So, $(7^{12})/(7^2)$ simplifies to $7^{(12-2)} = 7^{10}$ , which is not equivalent to $7^6$ .
Select the correct options: Select the correct options. $\newline$ From the evaluations, we see that options A and C are equivalent to $7^6$ . Therefore, the correct answers are A and C.