Integer Exponents Day 2

Warm UpFind the value of each power.

• Explore and apply the properties of integer exponents.

• Observe patterns to write the general rules of integer exponents.

• Then use these properties to generate equivalent numerical expressions.

• Recognize that there are patterns of integer exponents.

• Make conjectures about the properties of integer exponents.

• Apply the properties of integer exponents to simplify numerical expressions.

To apply the properties of exponents, the bases must be the same. However, some expressions can be manipulated to convert unequal bases. Consider the

following examples. Try simplifying each expression by manipulation.

To develop the properties of integer exponents, look for

patterns in a powers table, in the multiplication and division of

powers with the same base, and in powers of products. The

properties can be used to simplify complicated expressions.

Use your knowledge of the order of operations to help simplify

expressions involving exponents by simplifying what you can inside parentheses, and then use the

properties of exponents to simplify terms with exponents.

(-a)2 is always positive because the square of any nonzero number is

always positive.

The order of operations means -a2 = -( a2), and its value will always

be negative.

Simplify each expression.

To simplify an expression with exponents by applying the properties of exponents the order of operations must always be

followed. Each expression within brackets or parentheses must be

simplified first. Then terms with the same base that are being multiplied or

divided can be simplified using the properties of exponents. Finally, any terms being added or subtracted are

simplified.

A negative exponent does not mean the answer will be a negative

number.

When no exponent is given, it is understood that the number is

raised to the power of one.

Explain why the exponents cannot be added in the product .

The distance from Earth to the moon is about 224 miles. The

distance from Earth to Neptune is about 227 miles. Which distance is

the greater distance, and about how many times greater is it?

In computer technology, a kilobyte is 210 bytes in size. A gigabyte is

230 bytes in size. The size of a terabyte is the product of the size

of a kilobyte and the size of a gigabyte. What is the size of a

terabyte?

Exit TicketFind the value of each power.1. 5-2 2. 34

Use properties of exponents to write an equivalent expression.3. 4.

Simplify each expression.5. 6.