Roots & Exponents - Let's Review the Basics

Roots & Exponents

Let's Review The Basics

Square Roots of Positives

​Because...

8 x 8 = 64

and

-8 x -8 = 64

9 x 9 = 81

and

-9 x -9 = 81

Square Roots of Negatives

​Because...

The same number multiplied with itself is always positive

8 x 8 = 64

and

-8 x -8 = 64

Cube Roots

​Because...

4 x 4 x 4 = 64

and

-4 x -4 x -4 = -64

Other Odd Roots

​Because...

2 x 2 x 2 x 2 x 2 = 32

and

-2 x -2 x -2 x -2 x -2 = -32

Other Even Roots

of Positives

​Because...

3 x 3 x 3 x 3 = 81

and

-3 x -3 x -3 x -3 = 81

Other Even Roots

of Negatives

​Because...

When you multiply 4 of the same number together, it is always positive.

When you multiply 6 of the same number together, it is always positive.

Remember to multiply it with itself that many times.

Example: -3 exponent 4 is actually (-3)⁴

-3 x -3 x -3 x -3 = 81

Example: -2 exponent 3 is actually (-2)³

​-2 x -2 x -2 = -8

Exponents

​(x+5)²

is really

(x+5)(x+5)

Remember exponents always mean multilpy with itself

​Exponents on Other Things

Multiple Choice

(x-6)²

• x² - 36

• x² - 12x + 36

• 36x²

• -36x²

Multiple Choice

(6+x)²

• 36 + x²

• x² + 12x + 36

• 36x²

• -36x²

Multiple Choice

(6x)²

• x² + 36

• x² + 12x + 36

• 36x²

• -36x²

Multiple Choice

(-6x)²

• x² + 36

• x² + 12x + 36

• 36x²

• -36x²

Remember when solving equations to go backwards through PERMDAS

Adding cancels out subtraction (or negatives)

Subtraction cancels out adding (or positives)

Multiplying cancels out division (or denominators)

Dividing cancels out multiplying (number directly in front of something)

Exponents cancel out roots

Roots cancel out exponents

​Remember when solving, you put the exponent on each side, and simplify

Or put the root on each side,

and simplify

Multiple Choice

$$\left(4\ \ \sqrt[3]{x}\right)^3$$

• 4x

• 64x

• 4x³

• 64x³

Multiple Choice

$$\sqrt[]{\left(x+9\right)^2}\$$

• x+9

• x² + 81

• 9x

• x + 3

Remember your fractional exponents

Multiple Select

(2x+3)^5/3

• $$\sqrt[5]{\left(2x+3\right)^3}$$

• $$\sqrt[3]{\left(2x+3\right)^5}$$

• $$\left(\sqrt[5]{2x+3}\right)^3$$

• $$\left(\sqrt[3]{2x+3}\right)^5$$

If you had the last problem in an equation, you could pick how you wanted to re-write it, because there were two correct answers.

Then solve, remember to work outside in.

To cancel the root, do an exponent of the same value.

Then to cancel the exponent, do a root of the same value.

Open Ended

Write a few sentences, summarizing what your learned?

If you claim to learn nothing, write about what you need to make sure and memorize well for the test and future math classes.

Use details and explain some rules.