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)
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.”
Example 1: Application
One cup is 2–4 gallons. Simplify this expression.
A sand fly may have a wingspan up to 5–3 m. Simplify this expression.
7º = 1
In (–5)–4, the base is negative because the negative sign is inside the parentheses. In –5–4the base (5) is positive.
Evaluate the expression for the given value of the variables.
x–2 for x = 4
Substitute 4 for x.
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
B. denominator, such as
Example 4: Together
and denominator, such as
Example 4: Simplifying Expressions with Zero and Negative Numbers
PRACTICE: ON YOUR OWN denominator, such as
6.1 HOMEWORK denominator, such as
PG. 395 - 397
#24-42(all), 44-66(evens), 78-83, 100