Select all of the expressions that are equivalent to (3^6/3^−4)^2

Question

320
3 to the 20th power

12
12

60
60

34
3 to the 4th power

32×32
3 squared times 3 squared

310×310

Answer 1

To simplify the expression $(3^6/3^{-4}{)}^2$, we can start by applying the laws of exponents.

1. Simplify inside the parenthesis: $$3^6/3^{-4}=3^{6-(-4)}=3^{6+4}=3^{10}$$

2. Now raise it to the power of 2: $$(3^{10}{)}^2=3^{10\cdot 2}=3^{20}$$

Thus, the expression simplifies to $3^{20}$.

Now, let's evaluate each of the given expressions:

1. 320 - Not equivalent.
2. $3^{20}$ - Equivalent.
3. 12 - Not equivalent.
4. 60 - Not equivalent.
5. $3^4$ - Not equivalent.
6. $3^2\times 3^2$ - This is $3^{2+2}=3^4$, so it's not equivalent.
7. $3^{10}\times 3^{10}$ - This is $(3^{10}{)}^2=3^{20}$, so it’s equivalent.

The equivalent expressions are:

• $3^{20}$
• $3^{10}\times 3^{10}$

So the answers to the question are $3^{20}$ and $3^{10}\times 3^{10}$.