Square Roots & Estimating Square Roots, Solving Radical Equations LD, Radical Equations, Fractions & Exponents Math Skills, Fractional Exponents, Fractional Exponents

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Dividing Powers

Subtract the exponents and keep the base the same.

Negative Exponents

To change the sign cross the line. Find the reciprocal to make the exponent positive.

√324

18

(3ab)(6a⁴b⁶)

18a⁵b⁷

√361

19

√4

2

√400

20

√9

3

√64

8

(2x⁴x)³

8x¹⁵

√81

9

(3x⁰x³)²

9x⁶

(3y³)²

9y⁶

(y⁸y⁴)²

y²⁴

(y²)³

y⁶

(z⁷)²

z¹⁴

3¹/³

³√3

3²/³

(³√3)²

3⁴/³

(³√3)⁴

x⁴/³

(³√x)⁴

3³/⁴

(⁴√3)³

3⁵/⁴

(⁴√3)⁵

x³/⁴

(⁴√x)³

x²/⁵

(⁵√x)²

√1

1

√100

10

√121

11

√144

12

√169

13

√196

14

√225

15

√256

16

(4x²)²

16x⁴

(4x²x²)²

16x⁸

√289

17

(12x²)(3x)(x⁴)

36x⁷

(3x²y)(xy²)

3x³y³

(⁵√3)²

3²/⁵

(⁷√x)²

3²/⁷

√3

3¹/²

⁵√3

3¹/⁵

(√3)⁷

3⁷/²

√16

4

5x⁰

5

√25

5

√36

6

√49

7

Multiplying Powers

Add the exponents together and keep the base the same.

What is a radical equation?

An equation that contains at least one variable under a square, cubic, fourth etc. root

Power of a quotient

An exponent rule that says when you raise a quotient to a power you must raise the numerator and denominator to the power.

What is a radical expression?

An expression that contains at least one variable under a square, cubic, fourth etc. root

Zero Power

Any number raised to the zero power is equal to 1.

√110

Between 10 - 11

√145

Between 12 - 13

√220

Between 14 - 15

√245

Between 15 - 16

√290

Between 17 - 18

√333

Between 18 - 19

√376

Between 19 - 20

√19

Between 4 - 5

√46

Between 6 - 7

√75

Between 8 - 9

Power to a Power

Multiply the exponents together and keep the base the same.

What can never be x in the expression: √x ?

anything less than 0

break apart

count the number and variables for each problem put a parenthesis on each

when solving remember to start from

left to right then top to bottom

What is an extraneous root?

when a solution does not satisfy the root

Power of a Power

when raising a power to a power multiply exponents

Solve: 3√x =12

x = 16

Solve: √x - 4 = 10

x = 196

Solve: √(3x+4) - 3 = 1

x = 4

Simplify: √(x-2) / √(x-4)

x-2 / x-4

(³√x)²

x²/³

x⁵(x²x³)⁴

x²⁵

(√x)³

x³/²

(⁵√x)³

x³/⁵

(x³y²z⁵)(x⁵yz⁴)(x²y²)

x¹⁰y⁵z⁹

(x³)⁵

x¹⁵

(√x)⁵

x⁵/²

(³√x)⁵

x⁵/³

(x⁴)(x³)

x⁷

(xy)(x³y²)(x⁴y⁵)

x⁸y⁸

Simplify: x / √x - 4

x√x + 4x / x-16

3¹/⁴

⁴√3

3¹/⁶

⁶√3


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