Exponent & Radical Review and Practice

Exponent & Radical Review and Practice

by Jessica Kemmerer

Fill in the Blank

In this problem, what do we call the "2" ? $$2^4$$  

Fill in the Blank

In this problem, what do we call the "4" ? $$2^4$$  

Fill in the Blank

EVALUATE  $$2^4$$   (type your answer as a NUMBER)

Multiple Choice

Which number is the BASE? $$2^7$$ =128

• 2

• 7

• 128

• $$2^7$$  

​Exponent Rules

​These review 2 of our exponent rules:

​

​1) The multiplying rule

​

​2) The power to a power Rule.

​

​Review the rules before moving on.

Multiple Choice

$$x^3\cdot x^4\ =$$  

• $$x^{12\ }$$  

• $$x^{-1}$$  

• $$x^7$$  

• $$x^{34}$$  

Multiple Choice

$$10\times10\times10\times10\times10=$$  

• $$10\times5$$  

• $$10^5$$  

Multiple Choice

$$x^{-3}\cdot x^7\cdot x^2$$  =

• $$x^6$$  

• $$x^{12}$$  

• $$x^{-42}$$  

• $$x^{-12}$$  

Multiple Choice

$$\left(x^5\right)^4$$  

The power of a power rule says that when an exponential expression is raised to a power (as shown above), you should _________ the inner and outer exponents

• add

• subtract

• multiply

• divide

Multiple Choice

$$\left(x^7\right)^2$$  =

• $$x^{14}$$  

• $$x^9$$  

• $$x^5$$  

• $$2x^7$$  

Multiple Choice

(x⁴)²

• x⁸
• x⁶
• x²
• 8

​Exponent Rules Continued

​This rule says that if you have a bunch of things inside the parenthesis, make sure they ALL get the power that is on the outside.

​

​And make sure to MULTIPLY the POWERS.

Multiple Choice

(2⁵ * 2³)²

• 2¹⁶

• 2¹⁰

• 2¹¹

• 2¹⁷

Multiple Choice

((-2r)³)²

• (-2r)⁵

• -2r⁶

• 4r³

• 64r⁶

Multiple Choice

Simplify:
(5ab²)²

• 25a²b⁴
• 10a²b⁴
• 10ab⁴
• 25ab⁴

Multiple Choice

2.) Simplify
(3x³y⁵)⁴

• 3x¹²y²⁰
• 81x¹²y²⁰
• 12x¹²y²⁰
• 81x⁷y⁹

Multiple Choice

Simplify (-3x⁴y⁵)²

• 9x⁸y¹⁰
• 6x⁸y¹⁰
• -3x⁸y¹⁰
• -9x⁸y¹⁰

​Exponent Rules:

Zero & Negatives!

​Remember: anything to the 0 power is 1! (not 0)

​

​When dividing numbers, we SUBTRACT the EXPONENTS.

​

​But - If you have NUMBERS you divide them still.

​Quotient Rule Example

​1) Simplify the "x" values (7-3 = 4)

​

​2) Simplify the "y" values (5-2 = 3)

​

​3) The NUMBERS 24 and 8 are DIVIDED because they are just a normal fraction.

Multiple Choice

True or False: 

• True 
• False

Multiple Choice

Simplify the expression.

• 1
• g¹⁰
• g²⁵
• g

Multiple Choice

Evaluate using the quotient rule: 

• a⁸b¹³
• a²b⁷
• a¹⁵b³⁰

Multiple Select

Which are the same as

$$\frac{5^6}{5^3}$$  

Select 2 answers.

• $$5^9$$  

• $$5^3$$  

• $$125$$  

• $$5^2$$  

Multiple Choice

$$\frac{x^3y^{10}}{xy^{10}}$$  Simplify

• $$x^2$$  

• $$x^2y$$  

• $$\frac{x^2}{y}$$  

• $$x^4y^{20}$$  

Multiple Choice

Simplify $$\frac{10x^4}{15x^2}$$  .

• $$\frac{x^2}{5}$$  

• $$5x^2$$  

• $$\frac{2x^4}{3}$$  

• $$\frac{2x^2}{3}$$  

Multiple Choice

Simplify: $$\frac{x^{18}y^{15}}{x^6y^3}$$  

• $$x^3y^5$$  

• $$x^{12}y^{12}$$  

• $$x^{24}y^{18}$$  

• $$x^{108}y^{45}$$  

Fill in the Blank

$$5^0=$$  

Multiple Choice

• 2a²b⁶
• 1/2a²b⁶
• b⁶/2a²
• 2b⁶/a²

Multiple Choice

$$\left(\frac{a^2b^3}{c}\right)^3$$  

• $$\frac{a^6b^9}{c}$$  

• $$\frac{a^6b^9}{c^3}$$  

• $$\frac{a^8b^{27}}{c}$$  

• $$\frac{a^5b^6}{c^4}$$  

​Negative Exponents

​Remember that a negative exponent is like saying "repeated dividing"

​

​We can't leave an exponent negative. Move it to the other side of the fraction to make it positive.

Multiple Choice

Simplify

x⁻⁶

• $$\frac{1}{x^6}$$

• x⁶

• -x⁶

• $$\frac{-1}{x^6}$$

Multiple Choice

Rewrite using a positive exponent.

2w^-13

• -w¹³

• $$\frac{2}{w^{13}}$$

• $$\frac{2}{w^{-13}}$$

• $$2w^{13}$$

Multiple Choice

Simplify

• $$\frac{7a^5}{b^3}$$

• $$\frac{b^3}{7a^5}$$

• $$\frac{7b^3}{a^{-5}}$$

• $$\frac{7b^3}{a^5}$$

Multiple Choice

Write with positive exponents:

• a^-2

• a²

• $$\frac{1}{a^2}$$

Multiple Choice

Simplify the expression so that it contains only positive exponents.

Multiple Choice

Simplify. Hint: do product rule first, then negative rule!

• $$42x^5$$

• $$\frac{42}{x^5}$$

• $$\frac{42}{x^{-5}}$$

• $$\frac{1}{42x^5}$$

​Rational (fraction) Exponents and Radicals

Multiple Choice

Re-write the expression in radical form.
x^2/3

• ∛x²
• √x³
• $$\frac{1}{x}$$  

• ∛x

Multiple Choice

 Write in exponential form
 ∛x⁷

• $$x^{\frac{7}{3}}$$  

• $$x^{\frac{3}{7}}$$  

• 3x⁷
• 7x³

Multiple Choice

What is the value of 27^⅓?

• 27
• 9
• 3
• 1/3

Multiple Choice

Evaluate (find the number answer) the following expression:

• 5
• 25
• 125
• 625

Multiple Choice

Evaluate (find the number answer) the following expression:

• 2
• 8
• 16
• 32

Multiple Choice

Is the following statement is correct?

$$\left(-4\right)^{\frac{3}{2}}=8$$  

• True

• False

Multiple Choice

Which of these is correct?

• $$a^{-\frac{1}{2}}=-\frac{1}{a^2}$$

• $$a^{-\frac{1}{2}}=\frac{1}{\sqrt{a}}$$

• $$a^{-\frac{1}{2}}=-\sqrt{a}$$

Multiple Choice

Evaluate

$$\left(-8\right)^{\frac{2}{3}}$$  

• 1

• 2

• 3

• 4

Multiple Choice

$$64^{\frac{2}{3}}\ \$$ is the same as

• $$\ ^3\sqrt{64^2}\$$   so the answer is   8

• $$\ ^3\sqrt{64^2}\ \$$   so the answer is  16

• $$\ ^3\sqrt{64^2}\ \$$   so the answer is  4  

• $$64\ \times\frac{2}{3}\ \ \$$   so the answer is   $$\frac{32}{3}$$  

Multiple Choice

Write in exponential form  $$\sqrt[4]{\left(3x\right)^3}$$  

• $$3x^{\frac{3}{4}}$$  

• $$\left(3x\right)^{\frac{3}{4}}$$  

• $$\left(3x\right)^{\frac{4}{3}}$$  

• $$3x^{\frac{4}{3}}$$  

Multiple Choice

$$\sqrt[4]{m^3}$$  is the same as which answer?

• m^3/4
• m¹²
• m^4/3
• m⁷