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 \(3^{10} \times 3^{10}\).