There are (5^33)2⋅ 5^0 hens in a bird enclosure. What is the total number of hens in the enclosure?

Question

Group of answer choices

0

5^5

5^6

5^30

Answer 1

To find the total number of hens in the enclosure, we need to simplify the expression given: \((5^{33})^2 \cdot 5^0\).

First, simplify \((5^{33})^2\): \[ (5^{33})^2 = 5^{33 \cdot 2} = 5^{66} \]

Next, we note that \(5^0 = 1\). Therefore, we now have: \[ 5^{66} \cdot 5^0 = 5^{66} \cdot 1 = 5^{66} \]

Now, we need to compare \(5^{66}\) with the choices:

• \(0\)
• \(5^5\)
• \(5^6\)
• \(5^{30}\)

Clearly, \(5^{66}\) is not equal to any of the values given, and since \(66\) is greater than \(5\), \(6\), and \(30\), it denotes that there are more hens than the numbers in the choices provided.

Thus, the correct answer is none of the above choices, as \(5^{66}\) is not listed. If confined to the given responses, and none match \(5^{66}\), it indicates a potential oversight in the problem statement or answer choices provided.

Answer 2

pick one of the answer choices that are closest to the answer you've given.

Answer 3

The expression we simplified gives us \(5^{66}\), which is significantly larger than all the provided options. Among the options:

• \(5^5\)
• \(5^6\)
• \(5^{30}\)

The closest exponent is \(5^{30}\), since it is the largest of the choices listed, albeit still much smaller than \(5^{66}\).

So, if asked to choose the one that is the closest, I would select:

\(5^{30}\).