Foundations PT.2

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There are three properties of exponents that involve products:

Product of powers

Power of a product

Power of a power

a(3) x a(2)

a x a x a X a x a

= a(5)

EXAMPLE OF PRODUCT OF POWERS

ab(4)

ab x ab x ab x ab

Rearrange

( a x a x a x a ) x ( b x b x b x b)

a(4) b(4)

POWER OF A PRODUCT

a(2)5

a2 x a2 x a2 x a2 x a2

a x a a x a a x a a x a a x a

a(10)

POWER OF A POWER

Another Example:

x(-5) * x(4) (add exponents!)

x(-1) Simplify

1/x

Another Example:

(x(2)y(3))7

Changes to... x(2) *7 * y(3) *7

x(14) * y(21

ANOTHER EXAMPLE

TO GET RID OF NEGATIVE EXPONENT MOVE BASE TO DENOMINATOR AND CHANGE EXPONENT

(2xy)-3

1

______

(2xy)3

Now multiply every power

1

_____

(8x3y3)

In a repeating decimal, the digits underneath the bar repeat forever.

To represent an integer as a product of two other integers, think of the factors of that number.

Use the properties of exponents to help simplify exponential expressions.