Predict the result
Simplify three to the fourth power.
What does the exponent four tell you?

Set up the model
The base is three, and the exponent is four.
Multiply four factors of three; do not multiply the base by its exponent.

Work the example
Three times three is nine. Then nine times three is twenty seven.
Twenty seven times the last three is eighty one. So three to the fourth power is eighty one.

Check the result
Now simplify five cubed.
Count the factors of the base. Take eight seconds to think.
[Eight-second silent pause to work; the answer remains hidden.]
Five cubed means five times five times five.
The product is one hundred twenty five.

Interpret the result
For a positive integer exponent, count that many factors of the base.
Then multiply the factors. A power is not the base times the exponent.