Question

which expressions are equivalent to $7\cdot7\cdot7\cdot7\cdot7\cdot7$? choose 2 answers: a $\dfrac{7^8}{7^2}$ b $7^6\cdot7^1$ c $(7^2)^3$ d $\dfrac{7^{12}}{7^2}$

Explanation:

Step1: Simplify the original expression

The original expression $7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7$ is $7^6$ (since there are 6 factors of 7).

Step2: Evaluate Option A

Use exponent rule $\frac{a^m}{a^n}=a^{m-n}$:
$\frac{7^8}{7^2}=7^{8-2}=7^6$

Step3: Evaluate Option B

Use exponent rule $a^m \cdot a^n=a^{m+n}$:
$7^6 \cdot 7^1=7^{6+1}=7^7$

Step4: Evaluate Option C

Use exponent rule $(a^m)^n=a^{m \cdot n}$:
$(7^2)^3=7^{2 \times 3}=7^6$

Step5: Evaluate Option D

Use exponent rule $\frac{a^m}{a^n}=a^{m-n}$:
$\frac{7^{12}}{7^2}=7^{12-2}=7^{10}$

Answer:

A. $\frac{7^8}{7^2}$
C. $(7^2)^3$