Product of Powers, Power of a Power, and Power of a Product

How Many Miles Is a Light-Year?

If you were asked to give the distance between Richmond, VA and Charlotte, NC, you would probably give your answer in miles. A mile is a common unit used to measure large distances on Earth. In outer space, however, this common unit of measure is way too small to be useful. Instead, distances in outer space are measured in light-years, or in other words, the distance that light travels in a year.

If light travels at approximately 1.86 x 105 miles per second, and there are about 3.15 x 107 seconds in a year, how many miles does light travel in one year?

In order to answer this question, you will need to use your knowledge of the Product of Powers Property and scientific notation. If you multiply the distance that light travels in one second by the number of seconds in one year, you will be able to determine how many miles light travels in one year.

distance light travels in one year	=	distance light travels in one second	·	number of seconds in one year
	=	1.86 x 105	·	3.15 x 107

To multiply numbers in scientific notation, multiply the coefficients first. Then, multiply the powers by adding the exponents.

	=	1.86 · 3.15	·	105 · 107
	=	(5.859)	·	(1012)

You determined that light travels approximately 5.86 x 1012 miles in one year. In other words, a light-year is approximately 5.86 x 1012 miles.

 

Product of Powers

Consider the expression x³ · x². How would you simplify this expression? In this interactivity, you will learn how to apply the Product of Powers Property to multiply exponential expressions that have the same base. Click the player button to begin.

View a printable version of this interactivity.

Power of a Power

Consider the expression (x²)³. How would you simplify this expression? In this interactivity, you will learn how to apply the Power of a Power Property to raise a power to a power. Click the player button to begin.

View a printable version of this interactivity.

Power of a Product

Consider the expression (5x)³. How would you simplify this expression? In this interactivity, you will learn how to apply the Power of a Product Property to raise a product to a power. Click the player button to begin.

View a printable version of this interactivity.

 

 

 

Product of Powers, Power of a Power, and Power of a Product Review

Now that you have explored the Product of Powers, Power of a Power, and Power of a Product Properties, it is time to review your knowledge and practice what you have learned. Click the player button to get started.