Laws of Exponents - Multiplication and Division

Laws of Exponents

Multiplication and Division

Multiplying with exponents with the same base.

• Multiply the coefficients (Number in front of variable(s))

• ADD exponents with the same base.

EXAMPLE: Find the product.

5x²y (2x³y⁷)

• Mult. coefficents 5(2) = 10

• Add the exponents 2+3 = 5 and 1 +7 = 8

• Answer: 10 x⁵y⁸

Multiple Choice

In order to multiply powers with the same base, we add their exponents. 

• True 
• False

Multiple Choice

Simplify: $4x^5\cdot6x^{10}$  

•  $24x^{15}$  

•  $10x^{15}$  

•  $\sqrt{24x^{15}}$  

•  $\sqrt{10x^{15}}$  

Multiple Choice

Which expression represents the product of  $\left(2x^2y^2\right)\left(3x^3y^3\right)$ ?

•  $6x^6y^6$  

•  $5x^5y^5$  

•  $5x^6y^6$  

•  $6x^5y^5$  

Multiple Choice

The area of a rectangle is  $64a^8b^{13}$  square units. If the width if the rectangle is  $16ab^7$  units, what is the length?

•  $8a^8b^6$  

•  $4a^7b^6$  

•  $48a^7b^6$  

•  $1024a^9b^{20}$  

Dividing with exponents with the same base.

• Divide the coefficients (numbers in front of the variable)

• Subtract the exponents so that you have a positive exponent when you find the difference.

• Remember where the the remaining variable(s) are, denominator or numerator.

Example Dividing Exponents

• Find the quotient. 30a⁵b²/15a³b⁷

• Divide the coefficients 30/15 = 2

• Subtract the exponents with the remaining difference being positive. 5 - 3 = 2 and 7 - 2 = 5 (Note there are more "b"'s in the denominator do the reaming "b"s are in the denominator.

• Answer: 2a²/b⁵

Multiple Choice

According to exponent rules, when we divide two powers with the same base we _______ the exponents.
Example: h⁸ / h³

• add
• subtract
• multiply
• divide

Multiple Choice

8⁷ ⁄ 8²

• 8⁵
• 8⁹
• 8¹⁴
• 1⁵

Multiple Choice

8⁴ ⁄ 8⁶

• 1/8²

• 8²

• 8¹⁰

• 1/8¹⁰

Multiple Choice

• 1¹⁰

• 1²⁶

• z¹⁰

• z²⁶

Multiple Choice

• 8x⁴

• 8x⁸

• 6x⁴

• 6x⁸

Multiple Choice

• 2a²b⁶
• 1 / 2a²b⁶
• b⁶ / 2a²
• 2b⁶ / a²

MIXED REVIEW

Multiplying and dividing with exponents

Multiple Choice

n²⋅n⁴⋅n⁵

• n¹¹

• n⁴⁰

• n¹³

• n²²

Multiple Choice

Simplify:
b² ⋅ b⁴

• b⁸
• b⁶
• b²
• 2b⁶

Multiple Choice

Evaluate this expression using the quotient rule.

• 9⁵
• 9⁹
• 1⁵
• 9^-5

Multiple Choice

Evaluate the expression using the quotient rule.

• 2¹⁴ z¹³
• 2²/z⁷
• 2¹⁴/ z⁷
• 2² z⁷

Multiple Choice

Simplify (-4r⁵)(2r⁸)

• -8r¹³
• -2r¹³
• -8r⁴⁰
• -2y⁴⁰