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Video: Comparing the Values of Two Numbers Raised to Exponents and Evaluating Them

Kathryn Kingham

Louise and Andrea were trying to decide which is larger, 2⁸ or 8². Andrea guessed 2⁸ is larger, while Louise thought 8² is larger. Who guessed correctly? State the value for each.

02:23

Video Transcript

Louise and Andrea were trying to decide which is larger, two to the eighth power or eight squared? Andrea guessed two to the eighth power is larger, while Louise thought that eight squared is larger. Who guessed correctly? State the value for each.

To solve our problem, we will have to compare two to the eighth power to eight squared. We want to know which value is larger. This means we’re going to have to solve for each value.

It’s a bit easier to solve for eight squared. Eight squared just means eight times eight, and eight times eight equals sixty-four. To find out two to the eighth power, we need to multiply two by itself eight times.

If we start here, we can start by multiplying two times two; two times two is four; four times two is eight; eight times two equals sixteen; sixteen times two equals thirty-two; thirty-two times two equals sixty-four; sixty-four times two equals one hundred and twenty-eight; and finally one hundred and twenty-eight times two equals two hundred and fifty-six.

Two to the eighth power equals two hundred and fifty-six, and eight squared equals sixty-four. This means that two to the eighth power is much larger than eight squared. One part of our question is asking us to state the value for each, and we’ve done that here.

Now we need to answer the question, who guessed correctly? Andrea guessed that two to the eighth power is larger; Louise guessed eight squared is larger. Andre guessed correctly.