5.1 Use Properties of Exponents
Goal Simplify expressions involving powers.
Your Notes
VOCABULARY
Scientific notation
A number is expressed in scientific notation if it is in the form c10n where 1 c< 10 and n is an integer.
PROPERTIES OF EXPONENTS
Let a and b be real numbers and let m and n be integers.
Product of Powers Propertyam an = a__m + n__
Power of a Power Property(am)n = a__mn__
Power of a Product Property(ab)m =a _m_ b_m_
Negative Exponent Property
Zero Exponent Propertya0 = _1_ ,a
Quotient of Powers Property
Power of a Quotient Property
Example 1
Evaluate numerical expressions
a.(62)3 = 6 2 3 = 6 6= _46,656_
b.
c.
Your Notes
Example 2
Use scientific notation in real life
Iceland Iceland covers about 1.03 105 square kilometers and has approximately 2.94 105 people. About how many people are there per square kilometer?
Solution
Divide population by land area.
Quotient of powers property
Use a calculator.
= _2.85_Zero exponent property
There are about _3_ people per square kilometer.
Example 3
Simplify expressions
/ Power of a product property/ Power of a power property
=_x1515 y68_ / Quotient of powers property
=_x0y2_ / Simplify exponents.
=_y2_ / Zero exponent property
/ Negative exponent property
/ Power of a quotient property
/ Power of a power property
/ Negative exponent property
Your Notes
CheckpointEvaluate or simplify each expression.
1.
2.(4 103)(7 102)
280 or 2.8 102
3.(x2y6)7
4.
Example 4
Compare real-life volumes
Beach Ball The radius of a beach ball is about 5.6 times greater than the radius of a baseball. How many times as great as the baseball's volume is the beach ball's volume?
Solution
Let r represent the radius of the baseball.
/ The volume of a sphere is./ Power of a product property
=__5.63r0_ / Quotient of powers
=_5.63_ / Zero exponent property
176_ / Approximate power.
The beach ball's volume is about 176 times as great as the baseball's volume.
Homework
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