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Video: Writing a Numerical Expression as an Exponent Then Evaluating It

Kathryn Kingham

Write 5 × 5 × 5 × 5 using an exponent, and then find its value.

02:47

Video Transcript

Write five times five times five times five using exponents, then find its value.

An exponent is a small number placed above and to the right of a base number. The exponent refers to how many times the base number is multiplied by itself.

Our first step is to write five times five times five times five using exponents. Remember that our exponent is going to be the number of times that our base is multiplied by itself. Here, we’re multiplying five by itself four times. Four is our exponent. Four is our exponent and five is our base. If we multiply five by itself four times, another way to represent that is by saying five to the fourth power. We write it, five with an exponent of four. Five with an exponent of four.

This is not the only thing the question is asking us to do. The question also asks us to find its value. We need to calculate what five to the fourth power is. First, I noticed that five times five is twenty-five, and I’ve two groups of that. Now I need to calculate twenty-five times twenty-five. Here is one way we can try to solve this problem mentally. We can break twenty-five times twenty-five into two groups. First, we’ll calculate twenty-five times twenty, and then we’ll calculate twenty-five times five.

I know that twenty-five times four equals one hundred. I also know that twenty equals four times five. Twenty-five times twenty equals five hundred. Twenty-five times five is the next piece we need to solve. I easily recognized that twenty-five times four is one hundred. This means that twenty-five times five is going to be one hundred and twenty-five. The only thing left to do is to add five hundred and one hundred and twenty-five.

Twenty-five times twenty-five equals six hundred and twenty-five. Five to the fourth power equals six hundred and twenty-five.