Download Std 02 Exponent Notes

Exponent Notes
Std. 2.0 Students understand and use rules of exponents.
Multiplying Powers With Like Bases:
For any rational number a, and for all whole numbers m and n,
a  a = ______
m
n
When multiplying numbers with the same base, you _________ the exponents.
EX) x x  x
3
4
______
x
___
Dividing Powers With Like Bases:
For any rational number a (except a = 0), and for all whole numbers m and n,
am
n  _________
a
When dividing numbers with the same base, you _______________ the exponents.
x7
______
 x ___
EX) 3  x
x
Negative Exponents:
For any rational number a (except a = 0), and for all whole numbers m and n,
am 
1
or
1
m  __
a
All negative exponents can be written as positive exponents by doing the reciprocal (flipping the number over)
Ex) x
6
 _____
Ex)
1
3  ___
x
Exponent Notes
Std. 2.0 Students understand and use rules of exponents.
Multiplying Powers With Like Bases:
For any rational number a, and for all whole numbers m and n,
a  a = ______
m
n
When multiplying numbers with the same base, you _________ the exponents.
EX) x x  x
3
4
______
x
___
Dividing Powers With Like Bases:
am
For any rational number a (except a = 0), and for all whole numbers m and n, n  _________
a
When dividing numbers with the same base, you _______________ the exponents.

x7
______
 x ___
EX) 3  x
x
Negative Exponents:
For any rational number a (except a = 0), and for all whole numbers m and n,
am 
1
or
1
m  __
a
All negative exponents can be written as positive exponents by doing the reciprocal (flipping the number over)
 x
Ex)
6

 _____
Ex)
1
3  ___
x
Exponent = 0 (Zero Power):
0
a  1 For any rational number a (except a = 0). Any number raised to the zero power equals _____
EX) 5  ____
0
EX)
a4
44
 a ___  ____
4 a
a
Raising a Power to a Power:
m n
m n
For any rational number a, and for all whole numbers m and n, (a )  a
When a power is raised to a power, you ________________ the exponents.
Ex) (x )  x
9 3
______
x
___
Ex)
y   ____
5 6
Raising a Product to a Power:
n
n n
For any rational numbers a and b, and for any whole number n, (ab)  a b
Distribute the exponent to each term.
3 4
14 34
4 ___
3 2
Ex) (2x )  2 x  2 x 16 ___
Ex) (3x )  ____
Raising a Quotient to a Power:
a  an

For any rational numbers a and b (except b = 0), and for any whole number n,
b  bn
3
3
2m3  8m ___

x 

 ____
Ex)
Ex)  5   15
y 
 n 
n
n
Exponent = 0 (Zero Power):
0
a  1 For any rational number a (except a = 0). Any number raised to the zero power equals _____
EX) 5  ____
0
EX)
a4
44
 a ___  ____
4 a
a
Raising a Power to a Power:
m n
m n
For any rational number a, and for all whole numbers m and n, (a )  a
When a power is raised to a power, you ________________ the exponents.
Ex) (x )  x
9 3
______
x
___
Ex)
y   ____
5 6
Raising a Product to a Power:
n
n n
For any rational numbers a and b, and for any whole number n, (ab)  a b
Distribute the exponent to each term.
3 4
14 34
4 ___
3 2
Ex) (2x )  2 x  2 x 16 ___
Ex) (3x )  ____
Raising a Quotient to a Power:
a  an

For any rational numbers a and b (except b = 0), and for any whole number n,
b  bn
3
3
3


x
2m

8m ___





 ____
Ex)
Ex)
 15
5
y 
 n 
n
n
Practice from the textbook:
Pg. 207 (#13-22, #35-38)
Pg. 212
(#21-28)
Pg. 215
(#10-24)
Answers: