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