Exploring Division Properties of Exponents

Mr. Richards introduces division properties of exponents, covering key concepts like quotient of powers, power of a quotient, zero exponent property, and negative exponent property. He provides examples to illustrate each concept and concludes with a fun fact about the word 'zarf' and a discussion on order of magnitude.

What is the result of dividing c^{11} by c^8?

• c^3

• c^{19}

• c^{-3}

• c^8

How do you simplify x^7 y^{12} / x^6 y^3?

• x^6 y^9

• x y^3

• x y^9

• x^1 y^9

What is the power of the quotient (3/5)^4?

• 3^4 / 5^2

• 3^4 / 5^4

• 3 / 5^4

• 3^4 / 5

Simplify (4c^3d^2)^3 / 5^3.

• 64c^9d^6 / 125

• 64c^9d^6 / 25

• 4c^9d^6 / 125

• 64c^6d^9 / 125

What is any non-zero number raised to the zero power?

• Undefined

• Zero

• One

• The number itself

Simplify 12m^8n^7 / (anything)^0.

• Undefined

• One

• Zero

• 12m^8n^7

What is the reciprocal of a^{-n}?

• a^n

• 1 / a^{-n}

• a^{-n}

• 1 / a^n

Simplify x^{-4} y^9 / z^{-6} using positive exponents.

• x^4 y^9 z^6

• y^9 z^6 / x^4

• y^9 / x^4 z^6

• x^4 y^9 / z^6

What is the order of magnitude of 123,456?

• 10^3

• 10^6

• 10^5

• 10^4

How many orders of magnitude greater is 10^5 compared to 10^2?

• 10

• 5

• 3

• 2