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5.5 Negative Exponents & Scientific Notation
Example
Math 110 – Sections 5.5-5.7
Example 1. Simplify by writing each expression with
positive exponents only.
a) 5-3
b) 7 x −4
c) 2 -2 + 3−1
To write a number in scientific notation:
1. Move the decimal point in the original number to the
left or to the right so that the new number has a value
between 1 and 10.
2. Count the number of decimal places the decimal point
is moved. If the original number is 10 or greater, the
count is positive. If the original number is less than 1,
the count is negative.
3. Multiply the new number in Step 1 by 10 raised to an
exponent equal to the count found in Step 2.
x3
x7
Negative Exponents:
Scientific Notation
• Used to write numbers that are either very large or
very small
• A positive number is written as the product of a
number and an integer power of 10.
Example 2. Write each number in scientific notation:
a) 9,060,000,000
b) 0.0000017
1
Example 3. Write each number in standard notation,
without exponents.
a) 3.061× 10 -4
b) 6.00021 ×10 7
Example 4. Perform the indicated operation. Write each
result in standard decimal notation.
(
)(
a) 9 × 10 7 4 × 10 −9
)
b)
8 × 10 4
2 × 10 -3
Summary of Exponent Rules:
Example 5. Simplify by writing each expression with
If m and n are integers, and a, and b are real numbers:
positive exponents only.
Product Rule for Exponents:
a) a − 4b −7
(
)
−5
⎛ 9 x5 ⎞
⎟⎟
b) ⎜⎜
⎝ y ⎠
-2
c)
(3x
−2
)
y2
4 x y −2
-2
7
Power Rule for Exponents:
Power of a Product:
Power of a Quotient:
Quotient Rule for Exponents:
Zero Exponent:
Negative Exponent:
5.6 Division of Polynomials
Dividing a Polynomial by a Monomial
Divide each term of the polynomial by the monomial.
Example 1. Divide 25 x 3 + 10 x 2 by 5 x 2
2
Example 2. Divide 9 y − 12 y − 3 y
7
2
3y
2
Recall: Long division of whole numbers.
3661÷ 13
Example 5. Divide
6x2 + 7x − 7
2x −1
3 3
Example 3. Divide 12 x y − 16 xy + 2 y
4 xy
2
Example 4. Divide x + 12 x + 35 by x + 7 using long
division.
Example 6. Divide 5 − x + 9 x
3
3x + 2
3
4