6-1. Integer Exponents. Warm Up. Lesson Presentation. Lesson Quiz. Holt McDougal Algebra 1. Holt Algebra 1. Warm Up Evaluate each expression for the given values of the variables. 1. x 3 y 2 for x = –1 and y = 10 2. for x = 4 and y = (–7)
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Holt McDougal Algebra 1
Holt Algebra 1
Evaluate each expression for the given values of the variables.
1.x3y2 for x = –1 and y = 10
2. for x = 4 and y = (–7)
Write each number as a power of the given base.
3. 64; base 4
4. –27; base (–3)
Evaluate expressions containing zero and integer exponents.
Simplify expressions containing zero and integer exponents.
To simplify 32, use 3 as a factor 2 times: 32 = ???
ZERO OR NEGATIVE EXPONENTS
look for a pattern to figure it out.
When the exponent decreases by one, the value of the power is divided by 5.
Zero Exponents – Any nonzero number raised to the zero power is 1.
Negative Exponents– A nonzero number raised to a negative exponent is equal to 1 divided by that number raised to the opposite (postive) exponent.
Why “nonzero number” in the previous definition?
2–4 is read “2 to the negative fourth power.”
gal is equal to
Example 1: Application
One cup is 2–4 gallons. Simplify this expression.
Try this one yourself!!!
A sand fly may have a wingspan up to 5–3 m. Simplify this expression.
TRY THESE YOURSELF!!!
7º = 1
In (–5)–4, the base is negative because the negative sign is inside the parentheses. In –5–4the base (5) is positive.
Use the definition
Evaluate the expression for the given value of the variables.
x–2 for x = 4
Substitute 4 for x.
Example 3: Try another yourself!!!
Simplify the expression for the given values of the variables.
–2a0b-4 for a = 5 and b = –3
Substitute 5 for a and –3 for b.
Evaluate expressions with exponents.
Write the power in the denominator as a product.
Simplify the denominator.
for a = –2 and b = 6
Try these yourself!!!
Evaluate the expression for the given value of the variable.
1.) p–3for p = 4
What if you have an expression with a negative exponent in a denominator, such as ?
*Move the denominator to the top and change the sign
**An answer with a negative exponent IS NOT simplified fully
Example 4: Together
Example 4: Simplifying Expressions with Zero and Negative Numbers
PRACTICE: ON YOUR OWN
PG. 395 - 397
#24-42(all), 44-66(evens), 78-83, 100