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HERE IS A VIDEO TO START OUR LESSON.  ENJOY WATCHING!

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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) Write each number as a power of the given base.

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You have seen positive exponents. Recall that to simplify  3 2 , use  3  as a factor  2  times: 3 2  = 3    3 = 9.

But what does it mean for an exponent to be negative or 0? You can use a table and look for a pattern to figure it out.

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When the exponent decreases by one, the value of the power is divided by 5. Continue the pattern of dividing by 5.

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Base                        	      x                                     Exponent Remember!

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Integer Exponents
WORDS
NUMBERS
3 = 1 1230=1
Zero exponent—Any
nonzero number raised to
the zero power is I.
Negative exponent—A
32
nonzero number raised to a
negative exponent is equal
to 1 divided by that number
24 ¯ 16
raised to the opposite
(positive) exponent.
ALGEBRA
If x + O, then xo— I.
If x + O and n is an integer,
then —
¯ xn•

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Notice the phrase “nonzero number” in the previous table. This is because 0 0  and 0 raised to a negative power are both undefined. For example, if you use the pattern given above the table with a base of 0 instead of 5, you would get 0º =   . Also 0 –6  would be     =   . Since division by 0 is undefined, neither value exists.

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2 –4  is read “2 to the negative fourth power.”  Reading Math

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One cup is 2 –4  gallons. Simplify this expression.

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A sand fly may have a wingspan up to 5 –3  m. Simplify this expression.

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Any nonzero number raised to the zero power is 1.

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In (–3) –4 , the base is negative because the negative sign is inside the parentheses. In –3 –4  the base (3) is positive.  Caution

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Example 3A: Evaluating Expressions with Zero and Negative Exponents

Evaluate the expression for the given value of the variables.

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Example 3B: Evaluating Expressions with Zero and Negative Exponents

Evaluate the expression for the given values of the variables.

–2 a 0 b -4  for  a  = 5 and  b =  –3

Write the power in the denominator as a product.

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Evaluate the expression for the given value of the variable.

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What if you have an expression with a negative exponent in a denominator, such as            ?

So if a base with a negative exponent is in a denominator, it is equivalent to the same base with the opposite (positive) exponent in the numerator.

An expression that contains negative or zero exponents is not considered to be simplified. Expressions should be rewritten with only positive exponents.

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Example 4: Simplifying Expressions with Zero and Negative Numbers

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1.  A square foot is 3 –2  square yards. Simplify this expression.  Simplify. 		 2.  2 –6 3.  (–7) –3   4.  6 0

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Evaluate each expression for the given value(s) of the variables(s).

WELCOME TO GRADE 9 MATHEMATICS!

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