Call Now: (800) 537-1660
 Home    Why?     Free Solver   Testimonials    FAQs    Product    Contact

May 22nd

May 22nd

# Math 097 Lecture Notes

Algebra is the study of using symbols to express mathematical ideas . The topic in this
lesson is dividing monomials . Negative exponents will be introduced as a way to express
factors in the denominator .

Dividing with Exponents

Example:

In 1994, 532 billion cigarettes were sold in the United States. We would
write 532 billion as 532,000,000,000 or, using scientific notation, we
would write it as 5.32 x 1011.

In 1994 the Properties /adding-negative-numbers-on-ti.html">number of people in the U.S. 18 years old or older were 190
million. How many cigarettes sold per person in 1994?

If we write 190 million as 190,000,000 or 1.9 x 108, we can divide the
number of cigarettes sold by the number of people to find out how many
cigarettes sold per person.

(5.32 x 1011) / (1.9 x 108) = (5.32 /1.9) x 103 = 2.8 x 103 = 2800, so in 1994

2800 cigarettes sold per person.

Notice how eight factors of 10 cancelled from the numerator and denominator . In
general, when we have like factors in the numerator and the denominator, we can
combine them by subtracting exponents .

 Subtracting exponents

Examples simplify

We can apply the rule of subtracting exp onents to each different factor that appears in
both the numerator and the denominator of a fraction .
Example simplify

Example simplify

 Definition of zero exponent x0 = 1

Worksheet

 Simplify Solution

Worksheet with solutions

 Simplify Solution 3x2 2y3 cannot simplify further

When factors remain in the denominator, we use negative exponents

 Definition

Examples simplify and write without denominators

simplify and write without denominators

simplify and write without denominators

Fractions may be expressed both ways, either with negative exponents or with
denominators. It is important that algebra students can express fractions both ways.

When rewriting a factor with a negative exponent, move the factor to the other part of the
fraction and remove the negative.
Examples write without negative exponents

write without negative exponents

write without negative exponents

write without negative exponents

Summary

 Definitions x0 = 1 xnxk = xn+k Properties

Worksheet

 Simplify and write without negative exponents. Solution x2x3 x2 + x3 - 2(x3y)2 -2x-3 3y-4 ( 3x 2 / 2y ) 4 x2y-3

Worksheet with solutions

 Simplify and write without negative exponents. Solution x2x3 x5 x2 + x3 cannot simplify further - 2(x3y)2 - 2(x3y)(x3y) = -2x6y2 -2x -3 -2 / x3 3y-4 x2y-3
 Prev Next

Home    Why Algebra Buster?    Guarantee    Testimonials    Ordering    FAQ    About Us
What's new?    Resources    Animated demo    Algebra lessons    Bibliography of     textbooks