Intro to Rational Exponents

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

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

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Simplify:

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Simplify:

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Evaluate:

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Evaluate:

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Simplify:

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Multiply:
Write your answer as a reduced fraction!

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Multiply:
Write your answer as a reduced fraction!

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What is the exponent on this number: 7
Hint: it's invisible!

Every number or variable has an invisible exponent of 1. 

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

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

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

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

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

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

If 4\cdot4=16, then \sqrt{16}=4

If x^3\cdot x^3=x^6, then \sqrt{x^6}=x^3

If x^{\frac{1}{2}}\cdot x^{\frac{1}{2}}= x^1, then \sqrt{x^1}=

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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.

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To type the cube root symbol \sqrt[3]{} in your calculator, click: 
MATH  ->  4: \sqrt[3]{}

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Fill in the blank.

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

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

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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:

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Copy this in your notes:

Example similar to #22:

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Now you try!
No decimals!

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No decimals!

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Hint: Think (?)^ 4=81

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

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

Simplify:

Simplify:

Evaluate:

Evaluate:

Simplify:

Multiply: Write your answer as a reduced fraction!

Multiply: Write your answer as a reduced fraction!

What is the exponent on this number: 7Hint: it's invisible!

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

So we can say... x^{\frac{1}{2}}=\sqrt{x}​But why?? Let's recall the definition of square root:If 4\cdot4=16, then \sqrt{16}=4If x^3\cdot x^3=x^6, then \sqrt{x^6}=x^3If x^{\frac{1}{2}}\cdot x^{\frac{1}{2}}= x^1, then \sqrt{x^1}=

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.

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!

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

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

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

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:

Now you try!No decimals!

No decimals!

Hint: Think (?)^ 4=81Or to use your calculator, type 4 -> MATH -> 5: \sqrt[x]{}

Multiply:
Write your answer as a reduced fraction!

Multiply:
Write your answer as a reduced fraction!

What is the exponent on this number: 7
Hint: it's invisible!

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

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

If 4\cdot4=16, then \sqrt{16}=4

If x^3\cdot x^3=x^6, then \sqrt{x^6}=x^3

If x^{\frac{1}{2}}\cdot x^{\frac{1}{2}}= x^1, then \sqrt{x^1}=

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.

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:

Now you try!
No decimals!

Hint: Think (?)^ 4=81

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