Twa kɔ nsɛm atitiriw so
Log in
Sign up for FREE
arrow_back
Laabri

Intro to Rational Exponents

star
star
star
star
star
Last updated about 3 years ago
28 Nsɛmmisa
1
1
1
1
1
1
1
1
1

Today you're going to learn how to evaluate exponents that are fractions. For example:

1
1
1
1
1
1
1
1
1
1
1
1

Example similar to #22:

1
1
1
1
1
1
1

First, let's review the properties of exponents you learned last class:

Asemmisa {{asɛmmisaAhyɛnsode}}
1.

Forgot everything from last class? No worries! Watch the 3 min video above to see examples similar to #1-6.

Asemmisa {{asɛmmisaAhyɛnsode}}
2.

Simplify:

Asemmisa {{asɛmmisaAhyɛnsode}}
3.

Simplify:

Asemmisa {{asɛmmisaAhyɛnsode}}
4.

Evaluate:

Asemmisa {{asɛmmisaAhyɛnsode}}
5.

Evaluate:

Asemmisa {{asɛmmisaAhyɛnsode}}
6.

Simplify:

Asemmisa {{asɛmmisaAhyɛnsode}}
7.

Multiply:

Write your answer as a reduced fraction!

Asemmisa {{asɛmmisaAhyɛnsode}}
8.

Multiply:

Write your answer as a reduced fraction!

Asemmisa {{asɛmmisaAhyɛnsode}}
9.

What is the exponent on this number: 7

Hint: it's invisible!

Every number or variable has an invisible exponent of 1.

Asemmisa {{asɛmmisaAhyɛnsode}}
10.

Let's see if we can notice a pattern...

Try: 81^{\frac{1}{2}}=

Asemmisa {{asɛmmisaAhyɛnsode}}
11.

Asemmisa {{asɛmmisaAhyɛnsode}}
12.

Asemmisa {{asɛmmisaAhyɛnsode}}
13.

Therefore, raising a number to the 1/2 power, is the same as taking the of that number.

Asemmisa {{asɛmmisaAhyɛnsode}}
14.

So we can say... x^{\frac{1}{2}}=\sqrt{x}​

But why?? Let's recall the definition of square root:

Asemmisa {{asɛmmisaAhyɛnsode}}
15.

If we look REALLY CLOSE at the \sqrt{x} we'll start to see its invisible numbers...

Not only does it have an invisible exponent of 1 but there's also a 2 in the corner of the radical!

Using this pattern, select the true equation below.

Asemmisa {{asɛmmisaAhyɛnsode}}
16.

To type the cube root symbol \sqrt[3]{} in your calculator, click:

MATH -> 4: \sqrt[3]{}

Asemmisa {{asɛmmisaAhyɛnsode}}
17.

Fill in the blank.

27^{\frac{1}{3}}=

Asemmisa {{asɛmmisaAhyɛnsode}}
18.

Hint: use the cube root symbol in your calculator to evaluate.

Asemmisa {{asɛmmisaAhyɛnsode}}
19.

Asemmisa {{asɛmmisaAhyɛnsode}}
20.

Check out the difference between the examples below:

*It will always be easier to evaluate the radical first, then the exponent at the end.

Now you try:

Asemmisa {{asɛmmisaAhyɛnsode}}
21.

Copy this in your notes:

Asemmisa {{asɛmmisaAhyɛnsode}}
22.

Now you try!

No decimals!

Asemmisa {{asɛmmisaAhyɛnsode}}
23.

No decimals!

Asemmisa {{asɛmmisaAhyɛnsode}}
24.

Asemmisa {{asɛmmisaAhyɛnsode}}
25.

Asemmisa {{asɛmmisaAhyɛnsode}}
26.

Hint: Think (?)^ 4=81

Or to use your calculator, type 4 -> MATH -> 5: \sqrt[x]{}

Asemmisa {{asɛmmisaAhyɛnsode}}
27.

Asemmisa {{asɛmmisaAhyɛnsode}}
28.