Video: Using Laws of Powers to Evaluate Numbers Raised to Integer Powers

What is the value of (2⁻¹)⁴?


Video Transcript

What is the value of two to the negative first power to the fourth power?

We can solve this a few ways. Let’s first begin by solving this using the exponents. When exponents are right next to each other just as they are, we multiply. So we have two to the negative one times four power, which is two to the negative fourth power. However, when we have a negative exponent and a negative power, we can move it so it becomes positive.

So if two to the negative fourth is on the numerator, moving it to the denominator makes the exponent positive. If it would have been on the denominator. we’d move it up to the numerator and it would become positive. And two to the fourth power is 16. So our final answer is one 16th.

We also could have evaluated inside the parentheses first. Two to the negative first power, we can make the exponent positive by moving it to the bottom just as we said before. And now, two to the first power is two. So we have one-half to the fourth power. So one needs raise to the fourth power and so does two. And we get one 16th or one-half to the fourth power is the same as one-half times one-half times one-half times one-half, which again is one 16th. So our value is equal to one 16th.

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