Question

which expressions are equivalent to $6 \cdot 6 \cdot 6 \cdot 6 \cdot 6$?
choose 2 answers:
a $(6^2)^3$
b $2^5 \cdot 3^5$
c $\frac{6^6}{6^1}$
d $3^2 \cdot 2^3$

Explanation:

Step1: Rewrite original expression

$6 \cdot 6 \cdot 6 \cdot 6 \cdot 6 = 6^5$

Step2: Evaluate Option A

$(6^2)^3 = 6^{2 \times 3} = 6^6
eq 6^5$

Step3: Evaluate Option B

$2^5 \cdot 3^5 = (2 \cdot 3)^5 = 6^5$

Step4: Evaluate Option C

$\frac{6^6}{6^1} = 6^{6-1} = 6^5$

Step5: Evaluate Option D

$3^2 \cdot 2^3 = 9 \cdot 8 = 72$, $6^5=7776$, so $3^2 \cdot 2^3
eq 6^5$

Answer:

B. $2^5 \cdot 3^5$
C. $\frac{6^6}{6^1}$