warm-up: simplify. 1)2) evaluate each expression for the given values. 3) for x = –1 4) for x = 4...
TRANSCRIPT
Warm-up:• Simplify.
1) 2)
Evaluate each expression for the given values.
3) for x = –1 4) for x = 4
& y = 10 & y = (–7)
5) What is an integer?
Whole #s & their opposites (negatives)
Integer ExponentsZero Exponent &
Negative Exponents
Interactive
Algebra
Integer Exponents (vs. Fractional Exponents)
Draw & Complete the Table to make a conjecture about a zero exponent and negative exponents:
Power
Value 81 27 9 3 1
Zero Exponent
The Product of Powers Property:
1 does NOT mean !
The exponent does not turn into a 1
Zero Exponent
The Quotient of Powers Property:
1
Zero ExponentThe only number that can’t be raised to
the zero power is…
0Because
YOU CAN’T DIVIDE BY ZERO!
Zero ExponentAny nonzero number raised to the
zero power is 1.
–11
Negative Exponents
The Quotient of Powers Property:
1
Negative ExponentsAny nonzero number raised to a negative exponent
equals 1 divided by that number raised to the positive exponent. (RECIPROCAL)
A negative exponent does not mean tochange the sign of the number.
1 NOT
1
1
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Once the power with a negative exponent (UNHAPPY) moves to its proper location…
the exponent becomes positive because it is HAPPY it is in the correct place.
3
7–3
–7
EXAMPLE 1: Zero & Negative Exponents
1A)
1B)
1C)______
1D)______
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Fractions Raised to a Negative Exponent
Both numbers needto move places!
The exponents become positive after they move!
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Another way to simplify Fractions Raised to a Negative Exponent
FLIP IT!
The exponent becomes positive
after the flip!
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Fractions Raised to a Negative Exponent
FLIP IT!
EXAMPLE 2: Evaluating Expressions with Zero and Negative Exponents
Evaluate each expression for the given value(s) of the variable(s). 2A) for x = 4
NOT
Evaluate each expression for the given value(s) of the variable(s):
2B)
EXAMPLE 2: Evaluating Expressions with Zero and Negative Exponents
Evaluate each expression for the given value(s) of the variable(s):
2C)___________________________________
EXAMPLE 2: Evaluating Expressions with Zero and Negative Exponents
1
** When simplifying expressions with exponents:
• An expression that contains negative and/or zero exponents is NOT considered to be simplified!
• Exponents should be rewritten with only POSITIVE EXPONENTS.
Simplify:3A)
3B)
3C)
EXAMPLE 3: Simplify.The –4 only applies to the w since it is not ( )
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EXAMPLE 3: Simplify.Simplify.
3D)_________
3E)_________
3F)__________
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Warm-upShow the difference between the following:
1) and
2) and
Extra Practice Problems
Simplify.
1)
2)
Extra Practice Problems
Simplify.
3)
4)
Extra Practice Problems
Evaluate and then simplify.
5) when x = 15
3
Extra Practice Problems
Evaluate and then simplify.
6) when m = 4 & n = 7
Extra Practice Problems
Evaluate and then simplify.
7) when y = –9, w = 4, & x = 6
1
Extra Practice Problems
Simplify.
8)
9)
10)