**Name __________________________________ Date ___________________**
**LESSON 5.1**
**Study Guide**
**GOAL**
**Simplify expressions involving powers.**
**Vocabulary**
A number is expressed in **scientific notation** if it is in the form *c* 10^{n} where 1 *c* < 10 and *n* is an integer.
**EXAMPLE 1**
**Evaluate a numerical expression **
Negative exponent property
= 3^{6}(– 4)^{3} Power of a power property
= 729(–64) = – 46,656 Evaluate power.
**EXAMPLE 2**
**Use scientific notation in real life **
**Hoover Dam** The volume of concrete that was used to construct the Hoover Dam is about 3,325,000 cubic yards. One cubic yard of concrete weighs about 4050 pounds. About how many pounds of concrete were used to construct the Hoover Dam?
Pounds of concrete
Weight per cubic yard
Number of cubic yards
**Solution**
=
= 4050 3,325,000 Substitute Values
=(4,0510^{3})(3.32510^{6}) Write in scientific notation.
=(4,053.325(10^{3}10^{6}) Use multiplication properties.
=13.4662510^{9} Product of powers property
=1.34662510^{1}10^{9} Write 13.46625 in scientific notation.
=1.34662510^{10 }Product of powers property
The number of pounds of concrete is about 1.346625 10^{10}, or about 13,466,250,000 pounds.
**LESSON 5.1**
**Study Guide ***continued*
**EXAMPLE 3**
**Simplify an expression **
**Simplify the expression. Tell which properties of exponents you used.**
Power of a power property
Product of powers property
= *y*^{7}*z*^{0 }Quotient of powers property
= *y*^{7}.1 Zero exponent property
= *y*^{7 }Identity property of multiplication
**EXAMPLE 4**
**Compare real-life volumes **
**Softball** The radius of a softball is about times the radius of a baseball. How many times as great as the baseball's volume is the Softball's volume?
**Solution**
Let *r* represent the radius of a baseball. Then r represents the radius of a softball.
The volume of a sphere is πr^{3}
= Power of a product property
(cancel common factors)
= Power of a quotient and quotient of powers
= Zero exponent property
2.370370 Use a calculator.
The volume of a softball is about 2.37 times as great as the volume of a baseball.
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