MP2 Lesson 16 Rewriting Nth roots

Lesson 16 Rewriting Nth Roots

We will rewrite radical expressions that contains variables to equivalent forms.
I will summarize how to rewrite radical expressions into equivalent forms.
TEKS 2A.7G

Goal 1: Evaluating Nth Roots

​You can also write an nth root as a power of a. Let's look at the square root in particular.

​Definition of Square Root.

​Product of Powers property.

​Set exponents equal when bases are equal.

​Solve for k.

Math Response

How would you rewrite $$\sqrt[7]{x}$$

Type answer here

Correct Answer: x^{\frac{1}{7}}

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Rad

Let's talk rational exponents

Math Response

Rewrite this rational exponent: $$y^{-\frac{4}{3}}$$

Type answer here

Correct Answer: \frac{1}{\sqrt[3]{y^4}}

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Properties of Rational Exponents

​1.

2.

3.

4.

5.


6.

7. 8.

Math Response

Let's practice using the properties and rewriting exponents! Key is to SIMPLIFY as you start to apply properties of exponents to then rewrite.

$$\sqrt[3]{125y^6}$$

Type answer here

Correct Answer: 5y^2

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Math Response

Simplify:L $$\left(9u^2v^{10}\right)^{\frac{1}{2}}$$

Type answer here

Correct Answer: 3uv^5

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Math Response

Simplify: $$\sqrt[4]{\frac{x^4}{y^8}}$$

Type answer here

Correct Answer: \frac{x}{y^2}

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Math Response

Simplify: $$\frac{6xy^{\frac{1}{2}}}{2x^{\frac{1}{3}}z^{-5}}$$

Type answer here

Correct Answer: 3x^{\frac{2}{3}}y^{\frac{1}{2}}z^5

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Rad