What Do Fractional Exponents Imply? | by Brett Berry | Math Hacks

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Root notation from lesson twenty-one

The necessary function right here is the root index. Bear in mind the basis index tells us what number of occasions our reply should be multiplied with itself to yield the radicand.

A fractional exponent is an alternate notation for expressing powers and roots collectively. For instance, the next are equal.

We write the energy in numerator and the index of the basis within the denominator. If there isn’t a energy being utilized, write “1” within the numerator as a placeholder.

What would the next be equal to in radical notation?

For our functions, it doesn’t matter when you write the second energy on the 8 or on the dice root.

As a result of the dice root of 8 is 2, I want to take the basis first after which apply the facility.

In fact, the opposite order yields the identical end result.

What’s the following equal to in exponent notation?

That is equal to 2 raised to the 5/4’s energy.

If we need to, we will manipulate the above expression even additional. Start by recognizing that 5/4 is equal to 1 + 1/4.

Utilizing exponent properties from lesson twenty-nine, we will break up it into two expressions involving base 2.

From there drop the facility of 1 because it isn’t obligatory and rewrite the 1/4 energy as a root index of 4. Additionally be happy to drop the multiplication image.

Many occasions I’ve had college students come to me confused as a result of they couldn’t determine what they had been doing incorrect; their reply didn’t match the reply key. Typically the reply key had simplified the reply additional or wrote it in a unique format than the coed’s work. The scholar was appropriate however didn’t realize it!

Thanks for studying! For extra examples, together with examples involving algebraic expressions, see the video linked above.

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