Exponents

Laws of Exponents

Poll

Pick the one with the exponent.

• $$x^2$$  

• $$x_2$$  

• $$2x$$  

• $$\log_2x$$  

Multiple Choice

Write each product using an exponent.  7 x 7 x 7 x 7 x 7 x 7 x 7 x 7 

• 7⁷

• 7⁸

• 8⁷

• 7⁹

Multiple Choice

What operation do you use with exponents?

• addition

• subtraction

• multiplication

• division

Multiple Choice

Write each product using an exponent.  4 x 4 x 4 x 4 x 4 

• 4⁵

• 5⁴

• 4⁶

• 4⁶

Multiple Choice

Find the value (standard form) of the power.  3³

• 9

• 6

• 27

• 12

Multiple Choice

Rewrite using a positive exponent.
7^-10

• ¹/_7¹⁰
• 7¹⁰
• ¹/_7^-10
• -70

Multiple Choice

Rewrite using a positive exponent.
(-5)^-4

• (-5)⁴
• ¹/_(-5)^-4
• ¹/_(-5)⁴
• -625

Multiple Choice

Rewrite using a positive exponent.
g^-7

• ¹/_g⁷
• g⁷
• ¹/_g^-7
• -g⁷

Multiple Choice

Rewrite using a positive exponent.
w^-13

• -w¹³
• ¹/_w¹³
• ¹/_w^-13
• w¹³

Multiplication Rule

Add the Exponents for all like terms.

Symbols:
(a^x) × (a^y) = a^x+y
OR
(a²) × (a³) = a⁵

Multiplication Rule

Add the Exponents for all like terms.

Numbers:
2³×2⁵ = 2⁸ = 256
OR
7³ × 7^-1 = 7² = 49

Multiplication Rule

Add the Exponents for all like terms.

Numbers and Symbols:
-4y³×-5y² = 20y⁵
OR
2n³z⁴ × 3n²z = 6n⁵z⁵

Multiple Choice

Simplify the expression:  c⁴⋅c³=

• ^c12

• c⁴⁺³

• c⁷

Multiple Choice

Simplify the expression: 3x²⋅x²=

• 3x

• 3x²⁺²

• 3x⁴

Multiple Choice

(3⁴)(3⁷)

• 3²⁸

• 3³

• 3^-3

• 3¹¹

Multiple Choice

(x⁸)(x^-5)

• x^-40

• x^-13

• x¹³

• x³

Multiple Choice

Simplify. Your answer should contain only positive exponents. $$x^2\cdot x^4$$  

• $$x^2$$  

• $$x^6$$  

• $$x^{-2}$$  

• $$x^8$$  

Multiple Choice

Simplify. Your answer should contain only positive exponents. $$2a^2b^3\cdot4ab^2$$  

• $$8a^3b^5$$  

• $$2ab^2$$  

• $$8a^2b^5$$  

• $$\frac{1}{2}ab$$  

Multiple Choice

Simplify the expression: $$5x^9\cdot-6x^2$$  

• $$-30x^{11}$$  

• $$-30x^{18}$$  

• $$-x^{11}$$

• $$-x^{18}$$  

Multiple Choice

Simplify the expression: $$d^8\cdot d^{10}$$   

• $$d^2$$  

• $$d^{80}$$  

• $$d^{810}$$  

• $$d^{18}$$  

Multiple Choice

Simplify the expression: $$\left(2m^4\right)\left(5m^2\right)$$  

• $$10m^6$$  

• $$10m^8$$  

• $$7m^6$$  

• $$7m^8$$  

Division Rule

Subtract the Exponents for all like terms.

Symbols:
(a^x) / (a^y) = a^x-y
OR
(a⁸) ÷ (a³) = a⁵

Division Rule

Subtract the Exponents for all like terms.

Numbers:
2⁷ ÷ 2⁵ = 2² = 4
OR
7³ / 7¹ = 7² = 49

Division Rule

Subtract the Exponents for all like terms.

Numbers and Symbols:
-4y³÷-2y² = 2y
OR
9n⁷z⁴ / 3n²z = 3n⁵z³

Multiple Choice

Quotient/Division Rule

When dividing exponents with the same base, ________the exponents

• subtract

• divide

• add

• multiply

Multiple Choice

Simplify the expression.

• 7⁶
• 7^-5
• 1/7⁵
• 7⁵

Multiple Choice

Evaluate this expression using the quotient rule.

• 9⁵
• 9⁹
• 1⁵
• 9^-5

Multiple Choice

Which value is equivalent to the expression $$\frac{2^6}{2^3}$$ ? 

• $$2^2$$  

• $$2^3$$  

• $$2^9$$  

• $$2^{18}$$  

Multiple Choice

Simplify the following expression:

x¹⁸y¹⁵ / x⁶y³

• x³y⁵

• x¹²y¹²

• x²⁴y¹⁸

• x¹⁰⁸y⁴⁵

Multiple Choice

Simplify the following expression:

(x³y) ÷ (xy⁵)

• x²y⁴

• x³y⁴

• x²/y⁴

• x²/y⁵

Multiple Choice

Simplify the following expression:

a⁴ ÷ a¹²

• a³

• a¹⁶

• 1/a³

• 1/a⁸

Multiple Choice

Power to a Power Rule

When raising a power to a power, keep the base and ________ the exponents

• postive

• subtract

• multiply

• divide

Multiple Choice

Simplify the following expression:

(x⁵)⁴

• x⁹

• x²⁰

• x

• x⁵⁴

Multiple Choice

Simplify the following expression:

(b³)⁸

• b¹¹

• 8b³

• b²⁴

• 24b

Multiple Choice

Simplify. $$\left(m^3\right)^5$$  

• $$m^8$$  

• $$m^{15}$$  

• $$8m$$  

• $$15m$$  

Multiple Choice

Power of a Quotient Rule

When raising a quotient to a power, distribute the _____________ to the numerator and denominator. Then simplify the expression.

• exponent

• numbers

• integers

• name

Multiple Choice

Simplify

• x²⁸y¹² / x²y
• x²⁸y¹² / x⁸y⁴
• x²⁰y⁸

Multiple Choice

Simplify:
(12x⁵y⁴/16x²y⁶)^{2
Note: / is divide--rewrite first part over the second part to view easier}

• 9x⁹/16y⁴
• 144x¹⁰y⁸/256x⁴y¹²
• 3x^6/4y⁴
• 9x⁶/16y⁴

Multiple Choice

$$\left(\frac{3m^4}{m}\right)^3$$  

• $$3m^{12}$$  

• $$9m$$  

• $$27m^9$$  

• $$\frac{3}{m}$$  

Multiple Choice

(2⁵7³)⁸

• 2¹³7¹¹

• 2³7⁵

• 2⁴⁰7²⁴

• 2^-37^-5

Multiple Choice

$$\left(x^5y^7\right)^3\ =\ x^{15}y^{21}$$  

• True

• False

Mixed Practice

Multiple Choice

Which shows the Power Rule used correctly?  $$\left(ab\right)^5$$  

• $$ab^5$$  

• $$a^5b^5$$  

• $$a^5b$$  

• $$a^6b^6$$  

Multiple Choice

$$What\ is\ the\ base\ in\ 5^{6\ \ }?$$  

• 5

• 6

Multiple Choice

How would you represent 8⁶ ?

• 8 x 6
• 8 x 8 x 6
• 8 x 8 x 8 x 8 x 8 x 8
• 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6

Multiple Choice

2⁵ is the same as 2 x 5.

• True
• False

Multiple Choice

Find the equivalent expression.

9 x 9 x 9 x 9 x 9

• 9⁵
• 9¹⁵
• 9 x 5
• 9 + 9 + 9 + 9+ 9

Multiple Choice

What is the value of 4³?

• 12
• 7
• 64
• 16

Multiple Choice

Find the value of 2³

• 2
• 4
• 6
• 8

Multiple Choice

Simplify the expression: 3x²⋅x²=

• 3x
• 3x²⁺²
• 3x⁴

Multiple Choice

Simplify the expression: 
c⁴⋅c³=

• ^c12
• c⁴⁺³
• c⁷

Multiple Choice

x⁶ / x²

• x⁴

• x¹²

• x³

• x⁸

Multiple Choice

Multiple Choice

Multiple Choice

Anything raised to a power of zero is always: 

• 0
• 1
• itself
• negative

Multiple Choice

(5³x²y⁴)⁰

• 5xy
• 1
• 0
• 5

Multiple Choice

Simplify

(2a²b⁴z)(6a³b²z⁵)

• 8a⁵b⁶z⁶

• 12a⁶b⁸z⁵

• 12a⁵b⁶z⁶

• 8a⁶b⁸z⁵

Multiple Choice

Simplify

• x⁴/3

• 3x¹⁰

• 36x¹⁰

• 3x⁴

Multiple Choice

Simplify the following expression:

(x⁵)⁴

• x⁹

• x²⁰

• x

• x⁵⁴

Multiple Choice

$$\left(3n^4\right)^3$$  

• $$9n^{12}$$  

• $$9n^7$$  

• $$27n^7$$  

• $$27n^{12}$$  

Multiple Choice

(2ab)³

• 2³a³b³
• 2ab³
• 6a³b³
• 6ab