Question

select all the expressions that are equivalent to $3^7 \cdot 3$.
$\left(3^4\
ight)^2$ $\frac{3^8}{3^0}$
$\frac{1}{3^7}$ $\frac{3^7}{3}$

Explanation:

First, calculate the value of the original expression:
$3^7 \cdot 3 = 3^{7+1} = 3^8$.

Now evaluate each option:

1. $(3^4)^2 = 3^{4 \times 2} = 3^8$ (equivalent).
2. $\frac{3^8}{3^0} = \frac{3^8}{1} = 3^8$ (equivalent, since $3^0 = 1$).
3. $\frac{1}{3^7} = 3^{-7}$ (not equivalent).
4. $\frac{3^7}{3} = 3^{7-1} = 3^6$ (not equivalent).

Step1: Compute original expression

$3^7 \cdot 3 = 3^8$

Step2: Check each option

1. $(3^4)^2 = 3^8$; 2. $\frac{3^8}{3^0}=3^8$; 3. $\frac{1}{3^7}=3^{-7}$; 4. $\frac{3^7}{3}=3^6$

Step3: Select equivalents

Only $(3^4)^2$ and $\frac{3^8}{3^0}$ equal $3^8$

Answer:

$(3^4)^2$, $\frac{3^8}{3^0}$