Tamara texted a photo of a dolphin to 5 friends. She asked each of her 5 friends to text the photo to 5 more friends. The photo chain continued with each person texting the photo to 5 more friends. How many photos of the dolphin will be texted after 4 rounds? Write and evaluate an expression that shows the number of photos.

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To find the number of photos that will be texted after four rounds, we need to understand the pattern of how many photos are sent in each round.

In the first round, Tamara sent the photo to 5 friends. So, the number of photos in the first round is 1.

In the second round, each of the 5 friends received the photo and sent it to 5 more friends. Therefore, each friend sent the photo to 5 more friends, resulting in a total of 5 x 5 = 25 photos sent in the second round.

In the third round, each of the 25 friends received the photo and sent it to 5 more friends. Therefore, each friend sent the photo to 5 more friends, resulting in a total of 25 x 5 = 125 photos sent in the third round.

In the fourth round, each of the 125 friends received the photo and sent it to 5 more friends. Therefore, each friend sent the photo to 5 more friends, resulting in a total of 125 x 5 = 625 photos sent in the fourth round.

To summarize:

First round: 1 photo
Second round: 25 photos (5 friends x 5 photos each)
Third round: 125 photos (25 friends x 5 photos each)
Fourth round: 625 photos (125 friends x 5 photos each)

So, the total number of photos after four rounds is 1 + 25 + 125 + 625 = 776 photos.

The expression that shows the number of photos after 4 rounds is: 1 + (5^1) + (5^2) + (5^3) = 776.