Unit 7: Exponents
Lesson 7: Zero and Negative Exponents
Let’s Investigate
Zero Exponents
A nonzero number to the zero power is _____________.
Negative Exponents
The expression a-n is: ________________________________________
Example 1
Rewrite using positive exponents.
y-3 =
-2
3x
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y-4 z3
Unit 7: Exponents
Example 2
Simplify:
3 2 Example 3
Simplify:
2 ∙ Copyright © 2009-2010 Karin Hutchinson – Algebra-class.com
Unit 7: Exponents
Lesson 7: Zero and Negative Exponents – Practice Problems
Part 1: Rewrite using positive exponents.
1. x-4
4.
7.
2. 7y-3
-2 2
13.
8. y z
∙
6.
-4 2
-3
5. 3a b c
10.
3. (2x2)-2
9.
! 11.
14.
" # ∙ ! Simplify each expression.
)
1. "10& ' #( ∙ *) 2. ∙ Copyright © 2009-2010 Karin Hutchinson – Algebra-class.com
12.
! ! 15. x-2yz3 (x2y3z-4)
(3 points each)
3. (r2s-3t)-2 (rs3t-2)-3
Unit 7: Exponents
Lesson 7: Zero and Negative Exponents – Answer Key
Part 1: Rewrite using positive exponents.
1. x-4
+
,-
2. 7y-3
3. (2x2)-2
.
/0
Since 2x2 is in parenthesis, the
whole term is raised to the -2
power.
Only the y is raised to the
negative 3 power.
"
#
Then simplify the denominator.
1
+
= "2 #
-,
4.
5. 3a-2b2 c-3
X3
6.
Only take the reciprocal of
the variables with negative
exponents.
02
43 50
Make the exponent positive
by taking the reciprocal.
6
3
7 :
69
Then raise everything to the
3rd power.
20
3+;4;
7.
-4 2
8. y z
Make the exponent positive
by taking the reciprocal.
6
3 :
2
9.
Only take the reciprocal of
negative exponents.
<3
/-
Then raise everything to the
rd
3 power.
3.
=,0
Copyright © 2009-2010 Karin Hutchinson – Algebra-class.com
Since the power is positive,
raise everything to the 2nd
power first.
4 Then take the reciprocal of the
negative exponents only.
4 Simplify like terms.
4 (
Unit 7: Exponents
10.
11.
Divide by subtracting exponents of
like terms.
! ! /3,3 <0
12.
Make the exponent positive by
taking the reciprocal.
∙
Raise everything to the 2nd power.
Raise everything to the 3rd power.
9( 7 ? 9 7 ? 649 7 ? 279 7 ? Divide. (Subtract exponents)
Divide. (Subtract exponents)
9( 7 ? = 9( 7 ? 9 7 ? = 9 7 ? 649 7 ? 649 7 ? =
279 7 ? 27
649A 7 A ? (
=
27
14.
Step 1: Multiply (Add the exponents)
.
∙
=
(
DED E"#
20 2 =
Step 2: Divide (Subtract the exponents)
20 10 +C
=
=
2 /
Final Answer:
+C
/
49 7 ? 39 7?
4= 2;
53
! Make the exponent positive by
taking the reciprocal.
Take the reciprocal of negative
exponents only.
13.
! 9 7 ? 97? 1 "# =
2
2
Take the reciprocal of negative
exponents only.
" # ∙ ;-4B 2B
3.
Step 1: Take the reciprocal of the
first term in order to make
the exponent positive.
" #
1
∙ 15. x-2yz3 (x2y3z-4)
Step 1: Multiply (Add exponents)
x-2yz3 (x2y3z-4) = x-2+2y1+3z3+(-4)
=y4z-1
1
1
∙ Step 2: Multiply (Add exponents)
1
1
1
+
∙ = F F = 0 .
, /
Final Answer:
C0 is equal to 1, therefore, we
don’t need to write it in the final
answer.
+
,0 /.
Copyright © 2009-2010 Karin Hutchinson – Algebra-class.com
Step 2: Take the reciprocal of
variables with negative
exponents.
Final Answer: /<
/<
Unit 7: Exponents
Simplify each expression.
)
1. "10& ' #( ∙ *) Step 1: Rule – Any quantity raised to the
zero power is equal to 1. Therefore,
(10r7s11)0 = 1
Step 2: Take the reciprocal of any
quantity raised to a negative power in
order to make the power positive.
&' 1∙ '
**I know that if I multiply this
quantity by 1¸ my answer won’t
change. Therefore, I don’t need
to continue writing the 1.
Step 3: Raise the quantity to the 2nd
power.
& '
&'
= '
'
Step 4: Divide (Subtract the exponents)
& '
& ' =
= G3 H3
1
'
Final Answer: G3 H3
2. ∙ (3 points each)
Step 1: Take the reciprocal of the 2nd
fraction to make the power positive.
∙ 2 3. (r2s-3t)-2 (rs3t-2)-3
Step 1: Raise each quantity to
its’ respective power.
(r2s-3t)-2 (rs3t-2)-3 =
(r2(-2)s-3(-2)t-2) (r-3s3(-3)t-2(-3) =
Step 2: Raise the second fraction to the
2nd power.
(r-4s6t-2) (r-3s-9t6)
( ∙ 4 Step 2: Multiply (Add
exponents)
Step 3: Multiply (Add the exponents)
(r-4s6t-2) (r-3s-9t6) =
F( F
( ∙ = F F
4 4
= (
4 Step 4: Divide (Subtract the exponents)
(
=
=
(
4 4
4
Step 5: Take the reciprocal of any
negative exponents.
/I
= ;
-,
4
Final Answer:
/I
-,;
Copyright © 2009-2010 Karin Hutchinson – Algebra-class.com
r-4+-3s6+-9t-2+6 =
r-7s-3t4
Step 3: Take the reciprocal of all
negative powers.
JG. H0
Final Answer: JG. H0