2.1 Negative and Quotient Exponent Properties

2.1 Negative and Quotient Exponent Properties

by Christina Early

Multiple Choice

Simplify:  $$4a^3\cdot6a^8$$  

• 24a

• $$24a^{11}$$  

• $$4a^{11}$$  

• 12a*48a

Multiple Choice

Simplify: $$\left(2x\right)^5$$  

• $$10x^5$$  

• 2x⁵

• $$32x^5$$  

• 10x

​Negative Rule

aⁿ tells you to use a in a multiplication n times:

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​But those are positive exponents, what about something like:

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Negative? What could be the opposite of multiplying? Dividing!

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​A negative exponent means how many times to divide by the number.

​Examples: 8^-1 = 1 ÷ 8 = 1/8 = 0.125

​ 5^-3 = 1 ÷ 5 ÷ 5 ÷ 5 = 0.008

​Negative Rule Cont.

​But there is an easier way!

​5^-3 could also be calculated like:

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​That last example showed how to use the exponent property of negative exponents:

1. Calculate the positive exponent (aⁿ)

2. Then take the Reciprocal (i.e. 1/aⁿ)

Multiple Choice

Solve 5^-2

• -10

• 1/25

• 1/(5)²

• -1/10

Multiple Choice

3⁻⁴

• 1 ⁄ 81

• -81

• 81

• 1 ⁄ 12

Multiple Choice

Rewrite using a positive exponent. 2w^-13

• -w¹³

• 2/_w¹³

• 2/_w^-13

• 2w¹³

Multiple Choice

Simplify x⁻⁶

• 1 ⁄ x⁶

• x⁶

• -x⁶

• -1 ⁄ x⁶

​Quotient Rule

​The quotient rule says that if we have exponents with the same base being divided, we can just subtract the exponents. Ultimately this is about dividing exponential expressions. The formula is below:

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​Examples:

Multiple Choice

Quotient Rule: For LIKE BASES, keep the base the same and __________exponents.

• multiply

• add

• subtract

• divide

Multiple Choice

Simplify this expression using the quotient rule.

• 9⁵

• 9⁹

• 1⁵

• 9^-5

Multiple Choice

Simplify the expression.

• 7⁶

• 7^-5

• 1/7⁵

• 7⁵

Multiple Choice

$$\frac{\ \ \ x^{15}\ \ \ }{y^{12}}$$  

• $$xy^3$$  

• $$x^{27}$$  

• Not like bases, laws of exponents can not be applied 

• $$y^3$$  

Multiple Choice

$$\frac{18x^{10}}{2x^3}$$  Hint: divide coefficients

• $$9x^7$$  

• $$9x^{13}$$  

• $$18x^7$$  

• $$2x^{13}$$  

Multiple Choice

Simplify the expression so that it contains only positive exponents.

• $$\frac{1}{3x^3}$$

• $$\frac{3}{x^3}$$

• $$\frac{1}{-3x^3}$$

Extra Practice if time permits​

only if everyone finishes​

Multiple Choice

Evaluate the expression using the quotient of powers rule.

• a⁸b¹³

• a²b⁷

• a¹⁵b³⁰

• a⁸b⁷

Multiple Choice

• 3x^-1y^-5

• 3x²y

• 3xy⁵

• -3x³y⁷

Multiple Choice

Simplify. 2^-3 ⋅ 2^-4

• ¹/₁₂₈

• 2^-7

• 2¹²

• 2⁷

Multiple Choice

Simplify.

• y⁶⁰

• ¹/_y¹⁶

• y^-16

• y⁴

Multiple Choice

Write with positive exponents:

• a^-2

• a²

• $$\frac{1}{a^2}$$

• 2a

Multiple Choice

Evaluate

• -1

• 1/32

• -1/32

• 1

Multiple Choice

Simplify the following expression:

2x³y⁵ ⋅ 5xy²

• 10x⁴y⁷

• 7x⁴y⁷

• 10x³y¹⁰

• 7x³y¹⁰

Multiple Choice

Simplify the following expression:

(2a²b⁴z)(6a³b²z⁵)

• 8a⁵b⁶z⁶

• 12a⁶b⁸z⁵

• 12a⁵b⁶z⁶

• 8a⁶b⁸z⁵

Multiple Choice

Simplify the following expression:

(-4r⁵)(2r⁸)

• -8r¹³

• -2r¹³

• -8r⁴⁰

• -2y⁴⁰