How do you multiply powers with different bases but the same exponent?

You would multiply the bases and keep the exponent the same.

For example let's say you had 5³*7³. (5 and 7 are bases, 3 is the exponent)

If we break it down we can see what this problem is essentially saying.

5*5*5*7*7*7

Then, we can group the fives and the sevens since we have the same amount of each (due to having the same exponent).

(5*7)(5*7)(5*7)

Now, we can simplify this because it is a repeating pattern with equal amounts of each numbers.

(5*7)³

Next, solve inside the parenthesis.

(35)³

You can leave the answer like this, or solve to get 42,875.

This can be checked by expanding it and solving.

5³*7³
   ↓
5*5*5 = 125 and 7*7*7 = 343
              ↓
125*343 = 42,875