Law of exponents + rational exponents

Build your basis with law of exponents then move to the more advanced radical exponents. (will. require some prior knowledge on square roots)

x¹= ?

x

(-x)² = ? (ans)

x²

(-x)⁶ = ? (ans)

x⁶

(-x)³ = ? (ans)

-x³ or simplfied 1/x³

(-x)⁷ = ? (ans)

-x⁷

If -x (any negative variable) is raised by a ____ exponent it is always positive.

even (2,4,6)

If -x (any negative variable) is raised by a ____ exponent it is always negative.

odd (1,3,7)

7¹=?

7

50¹=?

50

x⁰=?

0

9⁰=?

0

-2⁰=?

0

a^-n=?

1/aⁿ

5^-2=? (use exponents rule)

1/5²

1/25

2^-8 × 2⁵=?

-8 + 5 = 3

1/2³

1/8

7^-2=?

1/7²

1/49

Positive exponents are ______ meaning negative exponents are ______

Multiplication, division

(x^m)ⁿ=?

x^mn

(x²)³=?

2×3=6

x⁶

Simplfy:

(x²)^-3

2x(-3)=-6

x^-6= 1/x⁶

(4⁴)^-2=?

4 x -2=-8

4^-8= 1/4^{8 (divide it by 1 to make positive)}

1/4⁸= 1/256

x^mxⁿ=?

x^m+n

2³2⁴=?

2³⁺⁴=2⁷

2⁷=128

x^mn=?

(x^m)ⁿ

x^m+n=?

x^mxⁿ

x^m/xⁿ=?

x^m-n

x^m-n=?

x^m/xⁿ

5³/5²=?

3-2=1

5¹=5

x⁴/x⁶

4-6=-2

x^-2= 1/x²

(xy)^m=?

x^my^m

x^my^m=?

(xy)^m

Simplify, not answer (7×8)²

7²8²

(x/y)ⁿ=?

xⁿ/yⁿ

x²/y²=?

(x/y)²

(4/2)³=?

4³/2³

2³=8

4³=48

48/8=6

1/aⁿ =?

a^-n

a^m/n =?

(ⁿ√a)^m or ⁿ√(a^m)

What is the index?

The number on the √ symbol

ⁿ√a=?

1/aⁿ

when simplifying radical expressions the ____ goes on the ___ and the ____ goes on the ____

exponent, top, square root, bottom

Solve ³√81 . Round to the nearest tenth.

³√81

81^1/3

4.3

Write √8 in simplest radical form

√8= √2×4

√2×4= √2 x √4

√4 = 2

2√2

Simplfy 8^4/3

8^4/3= ³√8⁴

³√8⁴=16

simplfy 16^3/4

16^3/4 = ⁴√16³

⁴√16³ = 8

A term is a ____ or ____

number, variable

Simplify the radical equation

⁴√16x¹²y¹⁰

⁴√16 ⁴√x^{12 4}√y¹⁰

16^1/4 x^12/4 y^10/4

2 x³ y^5/2

Simplify the radical equation

³√64x³y⁶

³√64 ³√x^{3 3}√y⁶

4 x^3/3 y^6/3

4 x¹ y²

Write the following expression in simplest exponential form (round).

³√81m²n

³√81 ³√m^{2 3}√n

4.3 m^2/3 n^1/3

Explain what a ration exponent, such as ^5/2 means.

the power of 5 over the square root of 2

9^5/2 =? (ans)

243

The expression ⁴√81x⁸y⁶ is equivalent to…

3x²y^3/2

simplify:

(8x⁶y²¹)^-1/3

1/(8x⁶y²¹)^1/3

1/8^1/3(x⁶)^1/3(y²¹)^1/3

8^1/3= ³√8

1/2x²y⁷

Given x>0 and y>0, select the expression that is equivalent to
³√-64x¹⁰y⁶

-4x^10/3y²

Given x>0 and y>0, select the expression that is equivalent to

√64x⁶y²

8x³y

If there is no number in the index than what would the blank space represent?: √

2

Given x>0 and y>0, select the expression that is equivalent to

⁴√256x¹⁶y¹²

4x⁴y³

Given x>0 and y>0, Write an expression that is equivalent to

⁴√81x²y¹⁸

3x^1/2y^9/2

Given x>0 and y>0, select the expression that is equivalent to

³√-64x¹²y⁴

-4x⁴y^4/3

skip

skip

Write the expression in radical form.

x^5/7

⁷√x⁵

Express (4³)^1/2 in simplest radical form

8

Express 18^1/4 in radical form

⁴√18

Simplify the following expression to simplest form using only positive exponents.

(8x⁶y²¹)^-1/3

1/ 2x²y⁷

When adding two variables with different exponents (EX: 3⁴+3² ) what do you do with the exponents?

You multiply them together. 6⁸

When multiplying two variables with different exponents (EX: 8⁵ x 8³ ) what do you do with the exponents?

You add them together. 8⁸

When dividing two variables with different exponents (EX: x⁴/x² ) what do you do with the exponents?

You subtract them. x²