Video: Evaluating an Expression with an Integer Base and a Positive Rational Exponent

Evaluate 243 ³ᐟ⁵.

01:57

Video Transcript

Evaluate 243 to the three-fifth power.

Okay, if you want my tip about how to answer something like this, here’s my tip: remember that a power to a power means multiply. And this is how that helps us here. I can take 243 and cube it and then take that value to the one-fifth power. Because I know that a power to a power means multiply and that three times one-fifth equals three-fifths, I know that I haven’t changed the value of this expression.

Once I break it apart into two pieces, we can evaluate them. We can take 243 to the third power, which equals 14348907. And then, we take that value and calculate it to the one-fifth power. 14348907 to the one-fifth power equals 27.

But this is why the trick I told you remembering a power to a power means multiply is so helpful. What if you had said instead you wanted to take 243 to the one-fifth power and then cube that value. One-fifth times three is still three-fifths. We should still end up with the same outcome. If you calculate 243 to the one-fifth power, you get three. And three cubed equals 27.

No matter which way you choose to operate, by remembering that a power to a power means multiply, you can always solve problems with fractional exponents.

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