Introduction to Rational Exponents

6-1: Rational Exponents and Properties of Exponents

Multiple Choice

$$3^{-3\ =}$$  

• -27

• $$\frac{1}{27}$$  

Multiple Choice

What does

$$2^{\frac{1}{3}}$$  =?

• $$\sqrt{2}$$  

• $$3\sqrt{2}$$  

Fill in the Blanks

x = ?

Fill in the Blanks

x = ?

 $256^{\left(x+2\right)}=\ 4^{\left(3x+9\right)}$  

Multiple Choice

Which is our first step to solve this?

• Set exponents equal to eachother

• divide

• create same base

• How should I know?!

Multiple Choice

What do we have now?

• $$4^{\left(x+2\right)}=\ 4^{\left(3x+9\right)}$$

• $$4^{\left(4\right)\left(x+2\right)}=4^{\left(3x+9\right)}$$

Multiple Choice

Next we distribute the 4 to get

• $$4^{\left(4x+8\right)}=4^{\left(3x+9\right)}$$

• $$4^{\left(4x+4\right)}=4^{\left(3x+9\right)}$$

Multiple Choice

Now, we....

• set the exponents equal to eachother

• get the same base

• divide

• I do not know

Now, we have

4x + 8 = 3x + 9

Fill in the Blanks

4x + 8 = 3x +9. x =

Multiple Choice

The same base will be...

• 2

• 4

• 8

Fill in the Blanks

next, we

Fill in the Blanks

now we set the

equal to eachother.

Try to solve

 $-\frac{3x}{2}+3=-\frac{2x}{3}$  

Fill in the Blanks

x =