Introduction to Radicals and Rational Exponents

Introduction Radicals and Rational Exponents

You know how to take exponents!

Multiple Choice

$$4^3$$  =

• 12

• 16

• 64

• 81

What if we wanted to "undo" the exponent?

Open Ended

Do you know how we can "undo" an exponent? Type your answer below!

Fill in the Blank

b² = 81. What is the value of b? (If you're not sure, say so!)

Fill in the Blank

$$x^3=64$$  . What is the value of x? (if you're not sure, say so!)

Poll

How confident are you with finding the root of a number?

• Super!

• Somewhat!

• Not there yet!

Converting Radicals to exponents.

• Fractional (rational) exponents are an alternate way to express radicals. If x is a real number and m and n are positive integers:

Converting Radicals to exponents.

• The denominator of the fractional exponent becomes the index (root) of the radical. The numerator of the fractional exponent becomes the power of the value under the radical symbol OR the power of the entire radical.

Multiple Choice

Rewrite the following

∛x⁵

• x^3/5

• x²

• x^5/3

• x³⋅x⁵

More examples

Last One

Multiple Choice

Which radical equation is equivalent to.. $$a^{\frac{1}{5}}$$  

• $$\frac{1}{\sqrt{a}}^5$$  

• $$\frac{1}{5}\sqrt{a}$$  

• $$5_{\sqrt{a}}$$  

• 5a

Simplifying

Remember your old properties of exponents when simplifying expressions.

Multiple Choice

Simplify

$$\left(3x^{-1}\right)^{\frac{2}{3}}=$$  

• $$^3\sqrt{\frac{x}{3}}$$  

• $$^3\sqrt{\frac{3}{x}}$$  

• $$3\sqrt{\left(\frac{x}{3}\right)^2}$$  

• $$^3\sqrt{\left(\frac{3}{x}\right)^2}$$  

Multiple Choice

$$\left(\frac{x^2}{x^{-11}}\right)^{\frac{1}{3}}$$  =

• $$x^3$$  

• $$^{13}\sqrt{x^3}$$  

• $$^3\sqrt{x^{13}}$$  

• $$^9\sqrt{x^3}$$  

What if you have variables?

1. Make sure the variable is an even power
2. If it's not even, subtract one from the exponent and rewrite as a product
3. Take the variable with the even power and divide by 2 - put that on the outside of the radical

Multiple Choice

Simplify.

Multiple Choice

Simplify the radical expression