Math Grade 10

Introduction to Exponents

​Exponential Form

• ​Exponential Form is a number made up of two pieces:

  • ​The base is the big, bottom number.

  • ​The exponent is the little number in the top right.

​What does an exponent mean?

​The exponent tells us how many times to multiply the base by itself.

​More examples...

​Solving with an exponent

​When solving for the final answer, take it step by step, multiplying two values at a time.

​10s Trick!!

When the base is 10, look at ​exponent, and that is how many zeros are in the answer!

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Multiple Choice

Evaluate: 6³

• 18

• 36

• 216

Multiple Choice

What is the base?

$$x^4$$  

• x

• 4

• There is no base.

Multiple Choice

Solve:  $$10^4$$  

• 10,000,000,000

• $$10,000$$  

• 40

• 1,000

• 100,000

Multiple Choice

Simplify the expression:

$$\left(5x^{11}\right)^2$$  

• $$25x^{22}$$

• $$10x^{22}$$

• $$25x^{13}$$

• $$10x^{13}$$

Multiple Choice

Simplify the expression:

$$\left(x^8\right)\left(x^{-5}\right)$$  

• $$x^{-40}$$  

• $$x^{-13}$$  

• $$x^{13}$$  

• $$x^3$$  
  

Multiple Choice

Simplify the expression:

$$\left(k^2\right)^5$$  

• $$k^7$$  

• $$k^3$$  
  

• $$k^{32}$$  
  

• $$k^{10}$$  
  

Multiple Choice

$$\left(-x\right)\left(-x\right)\left(-x\right)$$ is equivalent to which expression?

•  

  $$\left(-x\right)^3$$

• $$-x^3$$

Multiple Choice

$$\left(-8z\right)\left(-8z\right)\left(-8z\right)\left(-8z\right)$$ is equivalent to which expression?

•   $$\left(-8z\right)^4$$  

• $$-8z^4$$  

• $$-\left(8z\right)^4$$  

Laws of Exponents

a^-n is the reciprocal of aⁿ. For example, 4² and

4^-2 are inverses or reciprocals.

4²  = 4(4) = 16   4^-2 = 1 / 4(4) =1 / 16

If this is the case, if 3³ = 27, then 3^-3

Multiple Choice

If  $$3^{3\ }=\ 27,\ then\ 3\ ^{-3\ }=\ ?$$  

• $$\frac{1}{3^3}$$  

• -3

• -27

• $$\frac{1}{3^{-3}}$$  

Negative Exponents...

Multiple Choice

$$If\ 2^{-4}=\ \frac{1}{2^4},\ then\ 5^{-2\ }=\ ?$$   

• -25

• $$\frac{1}{5^2}$$  

• -5

• $$\frac{1}{5^{-2}}$$  

The power of 0

~ raising a nonzero number to the power of 0 = 1.

10⁰ = 1, 5⁰ = 1, -7⁰ = 1

Fill in the Blank

15⁰ = _____

Multiplying Exponents

When multiplying exponents, you simply add the exponents.

2³(2⁵) expanded out is 2(2)(2) times 2(2)(2)(2)(2)

You keep the base, 2, and add the exponents 3 + 5 = 8. 2³⁺⁵ = 2⁸

This rule applies to variables as well.

Multiple Choice

Simplify a⁴(a⁵).

• a⁴⁺⁵ = a⁹

• a^4-5 = a^-1

• a⁴⁽⁵⁾ = a²⁰

• 2a⁴⁺⁵ = 2a⁹

Dividing Exponents

Multiple Choice

$$\frac{12^6}{12^4}=\ ?$$  

• 12

• 1

• 
  $$12^{\left(6+4\right)}\ =\ 12^{10}$$  
  

• $$12^{\left(6\ -\ 4\right)}\ =\ 12^2$$  

Negative Exponents & Dividing Fractions

Fill in the Blank

$$Solve\ 4^{-3\ \div}\ 4^2$$  Write answer in standard form (as a whole number).

Multiple Choice

Evaluate this expression using the quotient rule.

• 9⁵
• 9⁹
• 1⁵
• 9^-5

Multiple Choice

(2ab)³

• 2³a³b³
• 2ab³
• 6a³b³
• 6ab

Multiple Choice

Evaluate the expression using the quotient rule.

• 3⁴
• 1/3⁴
• 3^-12
• 3³²

Multiple Choice

Simplify:
(x³)(x²)

• x⁵
• x⁶
• x
• x^1.5

Multiple Choice

Simplify:
2a⁷ ÷ 2a³

• a⁴
• 1/a⁴
• 2a⁴
• a^7/3

Multiple Choice

• -6c⁵
• -6c
• 6c
• -6c⁶

Multiple Choice

(2x³y)⁶

• 2x¹⁸y⁶
• 64x¹⁸y⁶
• 64x³y⁶
• 2x³y⁶

Multiple Choice

Simplify:
b² ⋅ b⁴

• b⁸
• b⁶
• b²
• 2b⁶

Multiple Choice

(x³y)⁶

• 2x¹⁸y⁶
• x¹⁸y⁶
• x³y⁶
• x³y⁶

Multiple Choice

• 4⁹
• 4⁴⁴
• 4²¹
• 4¹⁵

Multiple Choice

• w
• w^-1= 1/w
• -w
• w¹⁷

Multiple Choice

• a⁷
• a¹⁰
• a³
• a^-3

Multiple Choice

• 1
• 6⁰
• 36/36
• all of the above

Multiple Choice

$$\left(7x^3\right)^0$$  

• 1

• 7

• $$21x^3$$  

• $$x^{10}$$  

Multiple Choice

$$\frac{2x^4y^{-4}z^{-3}}{3x^2y^{-3}z^4}$$  

• $$\frac{2xyz}{3}$$  

• $$\frac{2x^2}{3yz^7}$$  

• $$\frac{2}{3}$$  

• NA

Multiple Choice

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

• ∛x²
• √x³
• (1/x)
• ∛x

Multiple Choice

 Write in exponential form
 ∛x⁷

• x⁷∕ ³
• x3⁄7
• 3x⁷
• 7x³

Multiple Choice

What is the value of 27^⅓?

• 27
• 9
• 3
• 1/3

Multiple Choice

Write the expression in exponential form:
√23

• 23^1/2
• 23^-1/2
• 23²
• 23^-2

Multiple Choice

Write the expression in exponential form:
∜x⁵

• x^4/5
• x^5/4
• x⁵
• x^1/4

Multiple Choice