Alg 2 Review 2

Exponent Rule - Rules that tell us how to simplify expressions with exponents.

​

Base - the number being multiply by itself

​

Exponent - a number telling how many times to multiply a number by itself.

mean 10⋅10

Multiple Choice

Which makes the statement true?

81⁰

• 81

• 9

• 1

• 0

Multiple Choice

Which makes the statement true?

345¹

• 300

• 0

• 345

• $$\frac{1}{345}$$

Multiple Choice

Which makes the statement true?

$$\left(\frac{1}{4}\right)^2$$

• $$\frac{1}{4}$$

• $$\frac{2}{8}$$

• $$\frac{1}{16}$$

• $$\frac{1}{8}$$

Multiple Select

Which makes the statement true? Choose 2 answer

$$5^{\frac{2}{3}}$$

• $$\sqrt[3]{25}$$

• $$\sqrt[3]{5^2}$$

• $$\sqrt[2]{9^3}$$

• $$\sqrt[]{81}$$

Multiple Choice

Which makes the statement true?

$$\left(\frac{3x}{y^2}\right)^2$$

• $$\frac{2x^2}{y^2}$$

• $$\frac{9x^2}{y^4}$$

• $$\frac{6x^{\ 2}}{y^3}$$

• $$\frac{2x^{ }}{y^3}$$

Multiple Choice

Which makes the statement true?

$$\left(4b\right)^{\frac{3}{2}}$$

• $$\sqrt[]{4^3b^3}$$

• $$\sqrt[3]{4b}$$

• $$\sqrt[]{4b^{ }}$$

• $$\sqrt[3]{16b^2}$$

Multiple Choice

Which makes the statement true?

2⁵ ⋅ 2^-2

• 16^-2

• 4¹⁴

• 16^-48

• 2³

Multiple Choice

Write the following expression in exponential form

$$\left(\sqrt[3]{5x}\right)^2$$

• $$\left(x\right)^{\frac{3}{2}}$$

• 
  $$\left(5x\right)^{\frac{2}{3}}$$

• $$5x^3$$

• 
  $$5x^{\frac{3}{2}}$$

Multiple Choice

What is the true statement

(4x^-6)² (3x^-4)

• 12x¹⁴

• 
  $$\frac{48}{x^{16}}$$

• 48x^-12

• 
  $$\frac{12}{x^{16}}$$

Solve The Radical Equation

1. ​Isolate the radical term on one side of the equation

2. Raise both sides of the equation to the power of the index of the radical (usually squaring for square roots)

3. Then Solve the resulting equation;

- Opposite Operations -
operations that "undo" each other, meaning they are essentially the inverse of one another.

​To Isolate the radical you do the opposite operation.

Solve The Radical Equation

​by subtract 3 on both side.

Multiple Choice

Does this Radical Isolate

$$\sqrt[]{x}+15=\ 20$$

• Yes

• No

Multiple Choice

How do we Isolate the Radical?

$$\sqrt[]{x}+15=\ 20$$

• Subtract the 15 on both side

• Add the 15 on both side

Multiple Choice

How do we remove the radical?

$$\sqrt[]{x}=\ 5$$

• by square on both side

• by subtract 5 to make it equal zero

Fill in the Blank

What is value for x? (Just the number)
$$\sqrt[]{x}=\ 5$$

Multiple Choice

Does this Radical Isolate?

• Yes

• No

Multiple Choice

What is the next step?

• $$\left(\sqrt[3]{5x\ -4}\right)^3\ =\left(\sqrt[3]{2x\ +5}\right)^3\$$

• (5x-4)³= (2x+5)³

Multiple Choice

What is the next step?

5x - 4 = 2x + 5

• 5x-2x = 5+4

• 5x-2x-4-5 = 0

Multiple Choice

What is the last step to solve for x?

3x = 9

• Divide by 3 on both side

• subtract 3x on both side

Multiple Choice

What is value of x?

3x = 9

• x = 3

• x = 5

• x = 9

• x = 27

Multiple Choice

Solve for x

$$\sqrt[3]{2x\ +\ 7}\ =\ 3$$

• x = 10

• x = 5

• x = 14

• x = 20

Multiple Choice

Solve for x

$$2\ \sqrt[]{x+5}+8=18$$

• x = 20

• x = 40

• x = 10

• x = 25

Multiple Choice

Solve for x

$$\sqrt[3]{4x\ -\ 3}=\sqrt[3]{3x\ +2}$$

• x = 5

• x = 9

• x = 12

• x = 3

Multiple Choice

Which is equivalent to the expression below?

$$\sqrt[]{25a^5b^9}$$

• 5a⁵b⁹

• 5a²b⁶

• $$5a^{\frac{5}{2}}b^3$$

• 25a²b⁶

Multiple Choice

Solve for P

$$x=\frac{\sqrt[3]{p}}{5}$$

• $$p=\frac{\sqrt[3]{x}}{5}$$

• p = (5x)³

• x = (p)³

• $$x=\ \frac{1}{5}$$

Product Property Radical

​Ex:

Quotient Property Radical

​Ex:

How to Simplify the radical

1. First factor the radicand (the expression under the radical) into its prime factors

2. then group any pairs of identical factors (since the index is usually 2 for square roots)

3. bring those factors out of the radical, and simplify the remaining expression under the radical by combining like terms.

​

1. First factor the radicand (the expression under the radical) into its prime factors

2. then group any pairs of identical factors (since the index is usually 2 for square roots)

3. bring those factors out of the radical, and simplify the remaining expression under the radical by combining like terms.

​= 4 ⋅ 2
= 8

​Example: 1

​Example: 2

​

1. First factor the radicand (the expression under the radical) into its prime factors

2. then group any pairs of identical factors (since the index is usually 2 for square roots)

3. bring those factors out of the radical, and simplify the remaining expression under the radical by combining like terms.

​Example: 1

​Example: 2

Multiple Choice

Multiply and Simplify the following radical expressions.

$$\sqrt[3]{64x^{15}}\ \cdot\ \sqrt[3]{6x^5}$$

• $$\sqrt[3]{70x^{20}}$$

• $$4x^6\sqrt[3]{6x^2}$$

• $$3x^8\sqrt[3]{2x}$$

• $$4x^2\sqrt[3]{3x^2}$$

Multiple Choice

Multiply and Simplify the following radical expressions.

$$\sqrt[3]{27x^{15}}\$$

• $$\sqrt[3]{70x^{20}}$$

• $$3x^4\sqrt[3]{x^2}$$

• $$3x^3$$

• $$4x^2\sqrt[3]{3x^2}$$

​Vertical Stretch vs Shrink

​Vertical Stretch - a > 1
Vertical Shrink - 0 < a < 1

Multiple Select

What is the transforming of this radical function? Choose 2 answers
$$y=\sqrt[]{x+3}-1$$

• vertical stretch

• reflection over the x-axis

• left 3 unit

• down 1 unit

Multiple Select

What is the transforming of this radical function? Choose 3 answers
$$y=-4\ \sqrt[]{x-2}+3$$

• vertical stretch by factor of 4

• reflection over the x-axis

• right 2 unit, up 3 unit

• reflection over the y-axis

Multiple Choice

What is the equation of this function?

Note the parent function is f(x) =√x

• $$-\ \sqrt[]{x}$$

• $$\sqrt[]{x}$$

• $$2\ \sqrt[]{x}$$

• $$\sqrt[]{-\ x}$$

Multiple Choice

Base on this graph which equation below are correct?

• $$-\ 3\ \sqrt[]{x}\ +2$$

• $$\sqrt[]{x-2}+3$$

• $$\ \sqrt[]{x+2}-1$$

• $$-\ \sqrt[]{x}\ -1$$

Domain is all the x values possible within a function. To find the domain, focus on the x coordinate of the point of origin (which is the h value in the function equation, just remember the opposite sign rule for h)

​The range will be all the possible outputs within the function, so focus on the y coordinate of the point of origin (which is the k value in the function equation)

​List of way to write the Domain and Ranch

Multiple Select

What is the Domain and Range for this graph?

Choose 2 answers

• {x | x ≥ -5 }

• {y | y ≤ -1 }

• y ≥ -1

• x > 5

Multiple Choice

What is the Domain of this function?

• 0 < x ≤ ∞

• 0 ≤ x < ∞

• [-1, ∞)

• x ≤ ∞

Multiple Choice

What is the Range of this function?

• 0 < x < ∞

• 0 ≤ x ≤ ∞

• [-1, ∞)

• x ≤ ∞