Exponent Properties

Product Rule
(add exponents)

Multiple Choice

(c⁵)(c³)(c³)

• c⁴⁵
• 3c¹¹
• c¹¹
• 3c⁴⁵

Multiple Choice

(6x²)(-3x⁵)

• 18x⁷
• -18x⁷
• 18x⁷
• 3x⁷

Multiple Choice

$$3n^5\cdot5n^{10}$$  

• $$15n^5$$  

• $$8n^{15}$$  

• $$15n^{50}$$  

• $$15n^{15}$$  

Multiple Choice

$$\left(-x^3\right)\left(-5x\right)$$  

• $$5x^4$$  

• $$-5x^4$$  

• $$5x^3$$  

• $$-5x^3$$  

Quotient Rule
(subtract exponents)

Multiple Choice

• x¹³
• x⁵
• x³⁶
• x^-5

Multiple Choice

$$\frac{k^3}{5k}$$  

• $$5k^2$$  

• $$\frac{5}{k^2}$$  

• $$\frac{k^2}{5}$$  

• $$\frac{k^4}{5}$$  

Multiple Choice

• 2x⁶

• 2x

• 2x⁵

• 2x⁸

Multiple Choice

Simplify

  $$\frac{x^{12}}{x^2}$$  

•     $$x^{10}$$  

•      $$x^6$$  

•     $$1^{10}$$  

•     $$1^6$$  

Power Rule
(multiply exponents)

Multiple Choice

(x⁴)²

• x⁸
• x⁶
• x²
• 8

Multiple Choice

(2x⁴y⁷)³

• 6x⁷y¹⁰
• 6xy³²
• 8x¹²y²¹
• 8x⁷y¹⁰

Multiple Choice

$$\left(2m\right)^5$$  

• $$10m^5$$  

• $$32m^5$$  

• $$25m^5$$  

• $$\frac{1}{2m^5}$$  

Multiple Choice

$$\left(2a^3b^4c^3\right)^2\cdot\left(4a^2bc^3\right)$$  

• $$16a^8b^9c^9$$  

• $$8a^8b^9c^9$$  

• $$8a^6b^5c^6$$  

• $$16a^5b^5c^6$$  

Negative Exponent
(flip and change sign)

Multiple Choice

x^-3

• -x³

• 1 / x³

• 1 / x^-3

• -x^-3

Multiple Choice

xy^-7

• xy⁷
• x/y⁷
• x⁷/y
• x⁷y

Multiple Choice

1/a^-2

• a^-2

• a²

• 1/a¹

Multiple Choice

4^-2= 

• 1/16
• -16
• 1/4
• -42

Multiple Choice

Zero Exponent
(anything to the zero power [except 0] is 1)

Multiple Choice

$$5^0$$  

• 5

• 1

• 0

• undefined

Multiple Choice

$$\left(\frac{5^3\cdot5^{-8}}{5^{-2}\cdot\left(5^3\right)^{-2}}\right)^0$$  

• 1

• 0

• $$5^3$$  

• $$\frac{1}{5^{13}}$$  

Multiple Choice

Multiple Choice

Simplify the expression shown. Your answer should contain only positive exponents.

• 4x⁶

• y⁴

• 32x⁵y⁴

• -4x⁷y³