All About Exponents

Powers and Exponents Summary

by Aqil Mohammed

Multiple Choice

What do you call the number 4 in 2⁴ ?

• Base

• Exponent

Multiple Choice

What do you call the number 3 in 3² ?

• Base

• Exponent

Multiple Choice

Which number is the BASE?
2³ = 8

• 2
• 3
• 8

Multiple Choice

Which is equivalent to 2⁴?

• 8
• 20
• 16
• 12

Multiple Choice

Write the expression using exponents:  $$j\times j\times j\times j\times j\times j$$  

• $$6j$$  

• $$j^6$$  

• $$6^j$$  

• $$j^5$$  

Multiple Choice

Write the expression using exponents:  $$9\cdot k\cdot k\cdot k\cdot k\cdot k$$  

• $$k^5$$  

• $$9k$$  

• $$k^9$$  

• $$9k^5$$  

Multiple Choice

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

• 4²
• 4³
• 4⁵
• 4⁶

Multiple Choice

Write each product using an exponent. 
12 x 12 x 12 

• 12¹
• 12³
• 12²
• 12⁴

Multiple Choice

Write each power as a product of the same factor. Then solve and find the value.
3³

• 3 x 3 x 3; 9
• 3 x 3 x 3; 27
• 3 x 3; 9
• 3 + 3; 6

Multiple Choice

Which is equivalent to 7 x 7 x 7 x 7 x 7 x 7 
?

• 7⁵
• 7⁶
• 6⁷
• 7⁷

Multiple Choice

$$10\times10\times10\times10$$  

Write the product as a POWER.

• $$4^{10}$$  

• $$10^4$$  

• $$40$$  

• $$14$$  

​Product of Powers:

Multiple Choice

10⁵ x  10⁷

• 10²
• 10³
• 10¹²
• 10¹³

Multiple Choice

t⁹  x  t⁸

• t¹
• t⁷²
• t¹⁷
• t

Multiple Choice

y¹²  x  y¹⁰

• y²
• y²²
• y²⁰
• y¹²⁰

​Quotient of Powers:

Multiple Choice

Evaluate this expression using the quotient rule.

• 9⁵
• 9⁹
• 1⁵
• 9^-5

Multiple Choice

Evaluate the expression using the quotient rule.

• 1²²
• 1³⁰
• 6²²
• 6³⁰

Multiple Choice

Simplify and write with positive exponents only. $$\frac{x^{10}}{x^2}$$  

• $$x^{18}$$  

• $$x^8$$  

• $$x^{20}$$  

• $$x^{12}$$  

Multiple Choice

Simplify the expression:

• $$c^7$$

• $$c^{-7}$$

• 7c

• -7c

Multiple Choice

Write the expression using exponents:

$$a\cdot a\cdot c\cdot c$$  

• $$a^2c^2$$  

• $$2a2c$$  

• $$\frac{1}{4}c^2d$$  

• $$\frac{1}{4}cd$$  

Multiple Choice

Write the expression using exponents: $$\frac{1}{4}\cdot c\cdot c\cdot d\cdot d$$  

• $$\frac{1}{4}cd^2$$  

• $$\frac{1}{4}c^2d^2$$  

• $$\frac{1}{4}c^2d$$  

• $$\frac{1}{4}cd$$  

Multiple Choice

$$2\cdot f\cdot f\cdot f\times3\cdot g\cdot g$$  

Write the expression using exponents

• $$23f^3g^2$$  

• $$2f^33g^2$$  

• $$6f^2g^3$$  

• $$6f^3g^2$$  

​Power of a Power Property

Multiple Choice

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

• add
• subtract
• multiply
• $$6f^3g^2$$  

Multiple Choice

(r⁴)⁶

• 10r
• $$2f^33g^2$$  

• $$6f^2g^3$$  

• $$6f^3g^2$$  

Multiple Choice

Which of the following expressions is equivalent to (2x)³ ?

• (2x)(2x)(2x)
• $$2f^33g^2$$  

• $$6f^2g^3$$  

• $$6f^3g^2$$  

Multiple Choice

Simplify:
(x³)²

• x⁵
• $$2f^33g^2$$  

• $$6f^2g^3$$  

• $$6f^3g^2$$  

Multiple Choice

If (2^x)⁵=2¹⁵, what does x equal?

• x = 3
• x = 5
• x = 10

​Power of a Product Property

Multiple Choice

(ab)²

• ab²
• a²b²
• a²b

Multiple Choice

(9xyz)⁸

• 72xyz⁸
• 72x⁸y⁸z⁸
• 9⁸x⁸y⁸z⁸
• 9/xyz⁸

Multiple Choice

Simplify the expression.  $$z^9\cdot n^9$$  

• $$\left(zn\right)^{18}$$  

• $$zn^9$$  

• $$\left(zn\right)^9$$  

• $$\left(zn\right)^{81}$$  

​What if we have to use both of these properties?

Multiple Choice

Simplify:
(5ab²)²

• 25a²b⁴
• 10a²b⁴
• 5a²b⁴
• 25ab²

Multiple Choice

Simplify:
(7y⁴)²

• 7y⁶
• 14y⁸
• 14y⁶
• 49y⁸

Multiple Choice

Simplify: (3x²)³

• 27x⁶
• 9x⁶
• 3x⁶
• 9x⁵

Multiple Choice

Simplify (-3x⁴y⁵)²

• 9x⁸y¹⁰
• 6x⁸y¹⁰
• 3x⁸y¹⁰
• -9x⁸y¹⁰

​Negative and Zero Exponents

Multiple Choice

Simplify 10⁰

• 10
• 1
• 0
• 100

Multiple Choice

Simplify (-9)⁰

• -9
• -1
• 1
• 9

Multiple Choice

Simplify y⁰

• y
• 0
• 1
• 1y

Multiple Choice

Simplify (-4x)⁰

• -4

• -4x

• -1

• 1

• 0

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

Multiple Choice

Rewrite each expression with a negative exponent.
¹/_12⁴

• ¹/_12^-4
• 12⁴
• ¹/_20,736
• 12^-4

Multiple Choice

Rewrite each expression with a negative exponent.
¹/_(-5)⁷

• (-5)⁷
• ¹/_(-5)^-7
• (-5)^-7
• ¹/_78,125

Multiple Choice

Rewrite each expression with a negative exponent.
¹/₁₂₅

• ¹/_5³
• 5³
• 5^-3
• ¹/_5-3

Multiple Choice

Simplify x²y^-5

• 1/x²y⁵
• x²/y⁵
• y⁵/x²
• x²/y^-5

Let's look at some harder problems

​Examples:

Multiple Select

$$Simplify\ \frac{2^3}{2^5}$$  

• $$2^{-2}$$  

• $$\frac{1}{2^2}$$  

• $$2^8$$  

• $$2^{35}$$  

Multiple Choice

Rewrite using exponents:  $$6^{-5}\times6^8$$  

• $$6^{-58}$$  

• 3

• $$6^3$$  

• $$6^{-40}$$  

Multiple Choice

Evaluate the expression: $$7^{-5}\div7^{-3}=$$  

• $$-\frac{1}{49}$$  

• -49

• 49

• $$\frac{1}{49}$$  

​Examples:

Multiple Choice

$$4^n\cdot4^{-2}\ =\ 16$$  

Find the value of n

• n = 4

• n = 8

• n = 2

• n = 0

Multiple Choice

$$\frac{3^3}{3^n}=3$$  

Find the value of n

• 1

• 0

• -2

• 2