Review of Exponent Rules

Basic Exponent Rules Review

Putting it all together!

Forms:

Multiple Choice

Which of the following is in standard form?

• 625

• $$5\cdot5\cdot5\cdot5$$

• 25(10+15)

• $$5^4$$

Multiple Choice

Which of the following is in exponential form?

• 625

• $$5\cdot5\cdot5\cdot5$$

• 25(15+10)

• $$5^4$$

Multiple Choice

Which of the following is in expanded form?

• 625

• $$5\cdot5\cdot5\cdot5$$

• 25(10+15)

• $$5^4$$

Multiple Choice

Which letter represents the base?

• A

• B

• C

Multiple Choice

5^{4 =}

• 4 x 4 x 4 x 4 x 4

• 5 x 4

• 5 x 5 x 5 x 5

Multiple Choice

In the expression 15⁸, what is the base?

• 8

• 15

Multiple Choice

Which letter represents the exponent?

• A

• B

• C

Multiple Choice

In the expression 15⁸, what is the exponent?

• 8

• 15

Multiple Choice

$$y^3\ =$$  

• 3 x 3 x 3

• (y) (y) (y)

Coefficient

Multiple Choice

Which letter represents the coefficient?

• A

• B

• C

Multiple Choice

In the expression, 3⁴, 3 is the ________, and 4 is the __________.

• exponent, base

• base, exponent

• power, base

• exponent, power

Fill in the Blank

What is the coefficient in the expression? $$5bf$$  

Multiple Choice

According to exponent rules, when we multiply powers we _______ the exponents.

• add

• subtract

• multiply

Multiple Choice

Simplify  $$h^2h^6$$  .

• $$h^8$$  

• $$h^{12}$$  

Multiple Choice

Simplify:  $$6^5\cdot6^2$$  

• $$6^7$$  

• $$6^3$$  

• $$36^7$$  

Multiple Choice

$$3^7\cdot3^7$$  

• $$9^{49}$$  

• $$3^{14}$$  

• $$3^{49}$$  

Multiple Select

Simplify the expression: r⁶⋅r²⋅r³=

(2 correct answers)

• r⁶⁺²⁺³
• r¹¹
• 11r
• r³⁶

Multiple Choice

$$x^5\cdot x^{10}=x^?$$  

• 2

• 5

• 50

• 15

Fill in the Blank

What will be the coefficient of the simplified expression?

$$\left(-2a^2b\right)\left(7a^3b\right)$$  

Fill in the Blank

What will be the exponent on b of the simplified expression?

$$\left(-2a^2b\right)\left(7a^3b\right)$$  

Multiple Choice

Select the simplified expression

$$\left(-2a^2b\right)\left(7a^3b\right)$$  

• $$-14a^6b$$  

• $$-14a^6b^2$$  

• $$-14a^5b^2$$  

• $$-14a^5b^{ }$$  

Multiple Choice

Simplify (2m⁴)(5m²)

• 10m⁶

• 10m⁸

Multiple Choice

Simplify: $$3x^5\cdot4x^2$$  

• $$12x^7$$  

• $$7x^{10}$$  

• $$12x^{10}$$  

• $$7x^7$$  

Multiple Choice

Simplify: $$3n^5\cdot5n^{10}$$  

• $$15n^5$$  

• $$8n^{15}$$  

• $$15n^{15}$$  

Multiple Choice

Simplify:  $$10x^8\cdot9x$$  

• $$90x^8$$  

• $$19x^9$$  

• $$90x^9$$  

Multiple Choice

Simplify: 3x³ ⋅ 3x

• 3²x⁴

• 3 ⋅ x ⋅ x ⋅ x ⋅3 ⋅ x

• 9x⁴

Multiple Choice

To simplify the expression below, you __________ the exponents. 

$$x^3\cdot x^4$$  

• add

• subtract

• multiply

• divide

Multiple Choice

X² ⋅ X³ ⋅ X⁴ ⋅ X

• x⁹
• x²⁴
• x¹⁰
• x²⁵

Multiple Choice

According to exponent rules, when we divide powers we _______ the exponents.

• add

• subtract

• multiply

Multiple Select

$$8^7\ \div\ 8^{5\ }=$$  

(choose all that apply)

• 8 x 8 x 8 x 8 x 8 x 8 x 8
  8 x 8 x 8 x 8 x 8

• $$8^2$$  

• $$8^{\left(7-5\right)}$$  

• 7 - 5

Multiple Choice

$$\frac{x^{10}}{x^5}=x^?$$  

• 15

• 5

• 50

• 2

Multiple Choice

Simplify the expression.

• 7⁶

• 7^-5

• 7⁵

Multiple Choice

Simplify: $$\frac{k^3}{5k}$$  

• $$5k^2$$  

• $$\frac{5}{k^2}$$  

• $$\frac{k^2}{5}$$  

#1

Multiple Choice

True or False?

• True
• False

Multiple Choice

Simplify

• 2x⁶

• 2x

Multiple Choice

Simplify:  $$\frac{15x^4y^4}{3x^3y}$$  

• $$12xy^4$$  

• $$18x^7y^5$$  

• $$5xy^3$$  

• $$5x^7y^4$$  

Multiple Choice

$$\left(x^3\right)^5$$  

To simplify the above expression, ___________ the exponents.

• add

• subtract

• multiply

• divide

Multiple Choice

$$\left(x^{10}\right)^{10}=x^?$$  

• 100

• 20

• 0

• 1

Multiple Choice

According to exponent rules, when we raise a power to a power we _______ the exponents.

• multiply

• subtract

• divide

Multiple Select

6² x 6² =

(choose all that apply)

• 6 x 6 x 6 x 6

• 6 x 2 x 6 x 2

• 6⁴

• (6²)²

Multiple Choice

(2⁸)²

• 2¹⁶

• 2¹⁰

Multiple Choice

Simplify: (m⁹)²

• m¹¹

• 2m⁹

• m¹⁸

Multiple Select

7³ x 7³ =

(choose all that apply)

• 7 x 3 x 7 x 3

• 7 x 7 x 7 x 7 x 7 x 7

• (7³)²

• 7⁶

Multiple Choice

Simplify: (m⁹)²

• m¹¹

• 2m⁹

• m¹⁸

Multiple Select

5² x 5³ =

(choose all that apply)

• 5 x 5 x 5 x 5 x 5

• 5 x 2 x 5 x 3

• 5⁵

Multiple Choice

$$\left(2xy\right)^3$$   In the above expression, the 3 applies to ________.

• only y

• 2, x, and y

• only x and y

• only 2

Multiple Choice

$$\left(2xy\right)^3=\ ?$$  

• $$2xy^3$$  

• $$2x^3y^3$$  

• $$8x^3y^3$$  

• $$8xy$$  

Multiple Choice

$$What\ numbers\ should\ go\ in\ place\ of\ the\ \Delta\ and\ O?$$   $$\left(4x^4\right)^2=\Delta\ x^O$$  

• 16, 16

• 16, 8

• 8, 8

• 8, 6

Multiple Choice

Simplify: (-5p)²

• -25p²

• 25p²

• -5p²

Multiple Choice

$$\left(-2x^3\right)^4$$  

• $$16x^{12}$$  

• $$-16x^{12}$$  

• $$8x^{12}$$  

• $$-8x^7$$  

• $$16x^7$$  

Multiple Choice

(3xy²z⁴)³

• 27x⁴y⁵z⁷

• 9x⁴y⁵z⁷

• 9x³y⁶z¹²

• 27x³y⁶z¹²

Multiple Choice

(-2xy²z⁴)⁵

• -10x⁶y⁷z⁹

• -10x⁵y¹⁰z²⁰

• -32x⁵y¹⁰z²⁰

• -32x⁶y⁷z⁹

Multiple Choice

$$\left(\frac{x}{y}\right)^4$$  

In the expression above, the exponent applies to which part or parts of the fraction?

• the numerator only

• the denominator only

• both the numerator and the denominator

• neither the numerator nor the denominator

Multiple Choice

$$\left(\frac{1}{3}\right)^2$$   What is the correct simplification of the above fraction? 

• $$\frac{2}{6}=\frac{1}{3}$$  

• $$\frac{1}{6}$$  

• $$\frac{1}{9}$$  

• $$3$$  

Multiple Choice

$$Simplify:\ \ \left(\frac{-2a^4}{b^{ }}\right)^3=$$  

• $$\frac{-6a^{12}}{b^3}$$  

• $$\frac{-8a^{12}}{b^3}$$  

• $$\frac{-8a^7}{b^4}$$  

Multiple Choice

$$Simplify:\ \ \left(\frac{-5a^4}{b^5}\right)2=$$  

• $$\frac{-10a^6}{b^{10}}$$  

• $$\frac{-25a^8}{b^{10}}$$  

• $$\frac{25a^8}{b^{10}}$$  

Multiple Choice

$$Simplify:\ \ \left(\frac{4a^7}{b^5c^4}\right)^3=$$  

• $$\frac{12a^{10}}{b^8c^7}$$  

• $$\frac{16a^{12}}{b^{20}c^{20}}$$  

• $$\frac{64a^{21}}{b^{15}c^{12}}$$